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Sep 21, 2013
09/13
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Ian I Kogan
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We are discussing some aspects of the magnetic monopoles and cosmic strings interactions with axion domain walss and membranes. The monopole moving through an axion domain wall is transformed into a monopole bag - the state with a dyon quantum number, but smaller mass. In the case of an axion membrane the passing monopole excites the chiral charged state at the membrane boundary. It will be shown that if cosmic string intersects an axion domain wall there will be $\theta = \pi$, i.e. maximal...
Source: http://arxiv.org/abs/hep-ph/9305307v1
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Sep 21, 2013
09/13
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Ian I. Kogan
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In this paper the several aspects of the $Z_{N}$ symmetry in gauge theories at high temperatures are discussed. The metastable $Z_{N}$ bubbles in the $SU(N)$ gauge theories with fermions may have, generically, unacceptable thermodynamic behavior. Their free energy $F \propto T^4$ with a positive proportionality constant. This leads not only to negative pressure but also to negative specific heat and, more seriously, to negative entropy. We argue that although such domains are important in the...
Source: http://arxiv.org/abs/hep-th/9311164v1
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Jul 19, 2013
07/13
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Ian I. Kogan
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We discuss a quantum \qa symmetry in Landau problem, which naturally arises due to the relation between the \qa and the group of magnetic translations. The last one is connected with the \w and area-preserving (symplectic) diffeomorphisms which are the canonical transformations in the two-dimenssional phase space. We shall discuss the hidden quantum symmetry in a $2+1$ gauge theory with the Chern-Simons term and in aQuantum Hall system which are both connected with the Landau problem.
Source: http://arxiv.org/abs/hep-th/9401093v2
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Sep 20, 2013
09/13
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Ian I. Kogan
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We discuss the $W_{\infty}$ symmetry in the $2+1$ gauge theory with the Chern-Simons term. It is shown that the generators of this symmetry act on the ground state as the canonical transformations in the phase space. We shall also discuss the analogy between discrete states in $c=1$ string theory and Landau level states in $2+1$ gauge theory with Chern-Simons term.
Source: http://arxiv.org/abs/hep-th/9208028v1
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Sep 18, 2013
09/13
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Ian I. Kogan
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We discuss the possibility that quantum black holes have discrete mass spectrum. Different arguments leading to this conclusion are considered, particularly the decoupling between left and right sectors in string theory - the so-called heterotic principle. The case of a $2+1$ dimensional black holes is considered as an argument in favour of this argument. The possible connection between membrane model of the black hole horizon and topological membrane is briefly discussed.
Source: http://arxiv.org/abs/hep-th/9412232v1
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Sep 21, 2013
09/13
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Ian I. Kogan
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Some exact static solutions for Einstein gravity in 2+1 dimensions coupled to abelian gauge field are discussed. Some of these solutions are three-dimensional analogs of the Schwarzschild black holes. The metrics in the regions inside and outside the horison are connected by the changing of the Planck mass sign.
Source: http://arxiv.org/abs/hep-th/9205095v1
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Sep 18, 2013
09/13
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Ian I. Kogan
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We discuss a possible relation between singletons in $AdS$ space and logarithmic conformal field theories at the boundary of $AdS$. It is shown that the bulk Lagrangian for singleton field (singleton dipole) induces on the boundary the two-point correlation function for logarithmic pair. Bulk interpretation of mixing between logarithmic operator $D$ and zero mode operator $C$ under the scale transformation is discussed as well as some other issues.
Source: http://arxiv.org/abs/hep-th/9903162v2
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Sep 17, 2013
09/13
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Ian I. Kogan
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This is a talk presented at XXXVIth Rencontres de Moriond, ElectroWeak Interactions and Unified Theories, March 2001. A short review of modern status of multigravity, i.e. modification of gravity at both short and large distances is given.
Source: http://arxiv.org/abs/astro-ph/0108220v2
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Sep 21, 2013
09/13
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Ian I. Kogan
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We consider the effective $1+1$-dimensional chiral theory describing fluctuations of the order parameter of the Disoriented Chiral Condensate (DCC) which can be formed in the central rapidity region in a relativistic nucleus-nucleus or nucleon-nucleon collisions at high energy. Using $1+1$-dimensional reduction of QCD at high energies and assuming spin polarization of DDC one can find the Wess-Zumino-Novikov-Witten (WZNW) model at level $k=3$ as the effective chiral theory for the...
Source: http://arxiv.org/abs/hep-ph/9305291v1
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Sep 23, 2013
09/13
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Ian I. Kogan
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We consider the quantum state describing the Disoriented Chiral Condensate (DCC) which may be produced in high energy collisions. Using the approach suggested by Rajagopal and Wilczek to describe the amplification of the long wavelength classical pion modes, we consider the quantum-mechanical evolution of the initial vacuum state into the final squeezed state describing the DCC. The obtained wave function has some interesting properties which are discussed.
Source: http://arxiv.org/abs/hep-ph/9310245v1
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Sep 23, 2013
09/13
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Ian I. Kogan
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We discuss the $2+1$ dimensional description of the $\Phi_{1,3}$ deformation of the minimal model $M_p$ leading to a transition $M_p \rightarrow M_{p-1}$. The deformation can be considered as an addition of the charged matter to the Chern-Simons theory describing a minimal model. The $N=1$ superconformal case is also considered.
Source: http://arxiv.org/abs/hep-th/9608031v1
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Sep 22, 2013
09/13
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Leith Cooper; Ian I. Kogan
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Using the topological membrane approach to string theory, we suggest a geometric origin for the heterotic string. We show how different membrane boundary conditions lead to different string theories. We discuss the construction of closed oriented strings and superstrings, and demonstrate how the heterotic construction naturally arises from a specific choice of boundary conditions on the left and right boundaries of a cylindrical topological membrane.
Source: http://arxiv.org/abs/hep-th/9602062v2
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Sep 19, 2013
09/13
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Thibault Damour; Ian I. Kogan
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We discuss the fully non-linear formulation of multigravity. The concept of universality classes of effective Lagrangians describing bigravity, which is the simplest form of multigravity, is introduced. We show that non-linear multigravity theories can naturally arise in several different physical contexts: brane configurations, certain Kaluza-Klein reductions and some non-commutative geometry models. The formal and phenomenological aspects of multigravity (including the problems linked to the...
Source: http://arxiv.org/abs/hep-th/0206042v2
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Sep 22, 2013
09/13
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Ian I. Kogan; Alex Kovner
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We apply a simple mean field like variational calculation to compact QED in 2+1 dimensions. Our variational ansatz explicitly preserves compact gauge invariance of the theory. We reproduce in this framework all the known results, including dynamical mass generation, Polyakov scaling and the nonzero string tension. It is hoped that this simple example can be a useful reference point for applying similar approximation techniques to nonabelian gauge theories.
Source: http://arxiv.org/abs/hep-th/9410067v1
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Sep 22, 2013
09/13
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Adel Bilal; Ian. I. Kogan
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After giving a pedagogical review of the chiral gauge approach to 2D gravity, with particular emphasis on the derivation of the gravitational Ward identities, we discuss in some detail the interpretation of matter correlation functions coupled to gravity in chiral gauge. We argue that in chiral gauge no {\it explicit} gravitational dressing factor, analogue to the Liouville exponential in conformal gauge, is necessary for left-right symmetric matter operators. In particular, we examine the...
Source: http://arxiv.org/abs/hep-th/9503209v1
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Sep 18, 2013
09/13
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Ian I. Kogan; Dimitri Polyakov
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Brane-like vertex operators, defining backgrounds with the ghost-matter mixing in NSR superstring theory, play an important role in a world-sheet formulation of D-branes and M theory, being creation operators for extended objects in the second quantized formalism. In this paper we show that dilaton's beta function in ghost-matter mixing backgrounds becomes stochastic. The renormalization group (RG) equations in ghost-matter mixing backgrounds lead to non-Markovian Fokker-Planck equations which...
Source: http://arxiv.org/abs/hep-th/0212137v3
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Jul 20, 2013
07/13
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Ian I. Kogan; Gloria Luzon
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In this letter we shall discuss a description of non-supersymmetric four-dimensional Yang-Mills theory based on Type 0 strings recently proposed by Klebanov and Tseytlin. The three brane near-horizon geometry allows one to study the UV behaviour of the gauge theory. Following Minahan and Klebanov and Tseytlin we shall discuss how the gravity solution reproduces logarithmic renormalization of coupling constant $g_e$ extracted from quark-antiquark potential and then show that effective coupling...
Source: http://arxiv.org/abs/hep-th/9902086v2
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Sep 18, 2013
09/13
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Ian I. Kogan; Dimitri Polyakov
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We discuss several closely related concepts in the NSR formulation of superstring theory. We demonstrated that recently proposed NSR model for superstrings on $AdS_5 \times S^5$ is described by the world-sheet logarithmic conformal field theory (LCFT). The origin of LCFT on a world-sheet is closely connected to the matter-ghost mixing in the structure of a brane-like vortex operators. We suggest a dynamical origin of M theory as a string theory with an extra dimension given by bosonised...
Source: http://arxiv.org/abs/hep-th/0012128v2
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Sep 20, 2013
09/13
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Ian I. Kogan; Alex Lewis
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A new relation between two-dimensional conformal field theories and three-dimensional topologically massive gauge theories is found, where the dynamical nature of the 3d theory is ultimately important. It is shown that the those primary states in CFT which have non-unitary descendants correspond in the 3d theory to supercritical charges and cause vacuum instability. It is also shown that logarithmic operators separating the unitary sector from a non-unitary one correspond to an exact zero...
Source: http://arxiv.org/abs/hep-th/9802102v3
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Sep 18, 2013
09/13
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Ian I. Kogan; Mikhail Shifman
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We argue that supersymmetric gluodynamics has two phases with equivalent infrared behavior, one of which is asymptotically free and another one is superstrongly coupled in the ultraviolet domain.
Source: http://arxiv.org/abs/hep-th/9504141v4
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Sep 17, 2013
09/13
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Ian I. Kogan; Alex Kovner
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We perform a variational calculation in the SU(N) Yang Mills theory in 3+1 dimensions. Our trial variational states are explicitly gauge invariant, and reduce to simple Gaussian states in the zero coupling limit. Our main result is that the energy is minimized for the value of the variational parameter away form the perturbative value. The best variational state is therefore characterized by a dynamically generated mass scale $M$. This scale is related to the perturbative scale $\Lambda_{QCD}$...
Source: http://arxiv.org/abs/hep-th/9408081v1
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Sep 19, 2013
09/13
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Ian I. Kogan; Dimitri Polyakov
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Brane-like vertex operators play an important role in a worldsheet formulation of D-branes and M-theory. In this paper we derive the DBI D-brane action from NSR closed string sigma-model with brane-like states. We also show that these operators carry RR charges and define D-brane wavefunctions in a second quantized formalism.
Source: http://arxiv.org/abs/hep-th/0208036v4
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Sep 22, 2013
09/13
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Ian I. Kogan; Alex Kovner
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We consider, from several complementary perspectives, the physics of confinement and deconfinement in the 2+1 dimensional Georgi-Glashow model. Polyakov's monopole plasma and 't Hooft's vortex condensation are discussed first. We then discuss the physics of confining strings at zero temperature. We review the Hamiltonian variational approach and show how the linear confining potential arises in this framework. The second part of this review is devoted to study of the deconfining phase...
Source: http://arxiv.org/abs/hep-th/0205026v1
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Sep 23, 2013
09/13
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Ian I. Kogan; Gloria Luzon
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The Maldacena's proposal has established an intriguing connection between string theory in AdS spaces and gauge theory. In this paper we study the effects of adding D(-1)-branes to the system of D3- or (D1-D5)-branes and we give arguments indicating that D(-1)-branes are necessary to describe four and two dimensional instantons.
Source: http://arxiv.org/abs/hep-th/9806197v3
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Jul 20, 2013
07/13
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Adel Bilal; Ian I. Kogan
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We study correlation functions in two-dimensional conformal field theory coupled to induced gravity in the light-cone gauge. Focussing on the fermion four-point function, we display an unexpected non-perturbative singularity structure: coupling to gravity {\it qualitatively} changes the perturbative $(x_1-x_2)^{-1}(x_3-x_4)^{-1}$ singularity into a logarithmic one plus a non-singular piece. We argue that this is related to the appearence of new logarithmic operators in the gravitationally...
Source: http://arxiv.org/abs/hep-th/9407151v1
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Sep 21, 2013
09/13
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Ian I. Kogan; Alex Lewis
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We study logarithmic operators in Coulomb gas models, and show that they occur when the ``puncture'' operator of the Liouville theory is included in the model. We also consider WZNW models for $SL(2,R)$, and for SU(2) at level 0, in which we find logarithmic operators which form Jordan blocks for the current as well as the Virasoro algebra.
Source: http://arxiv.org/abs/hep-th/9705240v2
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Sep 22, 2013
09/13
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Ian. I. Kogan; O. A. Soloviev
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We propose a world-sheet realization of the zigzag-invariant bosonic and fermionic strings as a perturbed Wess-Zumino-Novikov-Witten model at large negative level $k$ on a group manifold $G$ coupled to 2D gravity. In the large $k$ limit the zigzag symmetry can be obtained as a result of a self-consistent solution of the gravitationally dressed RG equation. The only solution found for simple group is $G=SL(2)$. More general target-space geometries can be obtained via tensoring of various cosets...
Source: http://arxiv.org/abs/hep-th/9807223v2
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Sep 18, 2013
09/13
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Ian I. Kogan; Ariel R. Zhitnitsky
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We analyse the highly excited states in $QCD_2 (N_{c}\rightarrow\infty) $ with adjoint matter by using such general methods as dispersion relations, duality and unitarity. We find the Hagedorn-like spectrum $\rho(m) \sim m^{-a}\exp(\beta_H m)$ where parameters $\beta_H$ and $a$ can be expressed in terms of asymptotics of the following matrix elements $f_{n_{\{k\}}} \sim \la 0|Tr(\bar{\Psi}\Psi)^{k}|n_{k}\ra$. We argue that the asymptotical values $f_{n_{\{k\}}}$ do not depend on $k$ (after...
Source: http://arxiv.org/abs/hep-ph/9509322v3
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Sep 19, 2013
09/13
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Ian I. Kogan; Richard J. Szabo
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We examine the relations between observables in two- and three-dimensional quantum gravity by studying the coupling of topologically massive gravity to matter fields in non-trivial representations of the three-dimensional Lorentz group. We show that the gravitational renormalization of spin up to one-loop order in these theories reproduces the leading orders of the KPZ scaling relations for quantum Liouville theory. We demonstrate that the two-dimensional scaling dimensions can be computed from...
Source: http://arxiv.org/abs/hep-th/9703071v1
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Sep 19, 2013
09/13
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Ian I. Kogan; John F. Wheater
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We consider new objects in bosonic open string theory -- ND tadpoles, which have N(euman) boundary conditions at one end of the world-sheet and D(irichlet) at the other, must exist due to s-t duality in a string theory with both NN strings and D-branes. We demonstrate how to interpolate between N and D boundary conditions. In the case of mixed boundary conditions the action for a quantum particle is induced on the boundary. Quantum-mechanical particle-wave duality, a dual description of a...
Source: http://arxiv.org/abs/hep-th/9703141v2
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Sep 22, 2013
09/13
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Ian I. Kogan; John F. Wheater
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We discuss the effect of boundaries in boundary logarithmic conformal field theory and show, with reference to both $c=-2$ and $c=0$ models, how they produce new features even in bulk correlation functions which are not present in the corresponding models without boundaries. We discuss the modification of Cardy's relation between boundary states and bulk quantities.
Source: http://arxiv.org/abs/hep-th/0003184v2
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Sep 22, 2013
09/13
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Ian I. Kogan; Graham G. Ross
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We consider a modification of gravity at large distances in a Brane Universe which was discussed recently. In these models the modification of gravity at large distances is ultimately connected to existence of negative tension brane(s) and exponentially small tunneling factor. We discuss a general model which interpolates between Bi-gravity model and GRS model. We also discuss the possible mechanism of stabilization for negative tension branes in AdS background. Finally we show that extra...
Source: http://arxiv.org/abs/hep-th/0003074v1
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Sep 19, 2013
09/13
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Ian I. Kogan; John F. Wheater
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We discuss some possible relationships in gauge theories, string theory and M theory in the light of some recent results obtained in gauge invariant supersymmetric quantum mechanics. In particular this reveals a new relationship between the gauge group E_8 and 11-dimensional space.
Source: http://arxiv.org/abs/hep-th/9911252v1
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Sep 21, 2013
09/13
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V. L. Eletsky; Ian I. Kogan
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The Goldberger-Treiman relation is shown to persist in the chiral limit at finite temperatures to order $O(T^2)$. The $T$ dependence of $g_A$ turns out to be the same as for $F_{\pi}$, $g_{A}(T)=g_{A}(0)(1-T^2/12F^2)$, while $g_{\pi NN}$ is temperature independent to this order. The baryon octet ${\cal D}$ and ${\cal F}$ couplings also behave as $F_{\pi}$ if only pions are massless in the pseudoscalar meson octet.
Source: http://arxiv.org/abs/hep-ph/9312255v1
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Sep 19, 2013
09/13
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William E. Brown; Ian I. Kogan
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We discuss three dimensional compact QED with a theta term due to an axionic field. The variational gauge invariant functional is considered and it is shown that the ground state energy is independent of theta in a leading approximation. The mass gap of the axionic field is found to be dependent upon theta, the mass gap of the photon field and the scalar potential. The vacuum expectation of the Wilson loop is shown to be independent of theta in a leading approximation, to obey the area law and...
Source: http://arxiv.org/abs/hep-th/9703128v2
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Sep 18, 2013
09/13
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P. Castelo Ferreira; Ian I. Kogan
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We study open and unoriented strings in a Topological Membrane (TM) theory through orbifolds of the bulk 3D space. This is achieved by gauging discrete symmetries of the theory. Open and unoriented strings can be obtained from all possible realizations of $C$, $P$ and $T$ symmetries. The important role of $C$ symmetry to distinguish between Dirichlet and Neumman boundary conditions is discussed in detail.
Source: http://arxiv.org/abs/hep-th/0012188v4
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Sep 19, 2013
09/13
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Ian I. Kogan; Kai-Ming Lee
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We discuss the structure of the vacua in $O(2)$ topologically massive gauge theory on a torus. Since $O(2)$ has two connected components, there are four classical vacua. The different vacua impose different boundary conditions on the gauge potentials. We also discuss the non-perturbative transitions between the vacua induced by vortices of the theory.
Source: http://arxiv.org/abs/hep-th/9506190v2
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Sep 19, 2013
09/13
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Ian I. Kogan; Richard J. Szabo
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We describe the structure of string vacuum states in the supersymmetric matrix model for M theory compactified on a circle in the large-N limit. We show that the theory admits topological instanton field configurations which at short-distance scales reduce to ordinary Yang-Mills instantons that interpolate between degenerate vacua of the theory. We show that there exists further classes of hadronic strings associated with the D-string super-fields. We discuss the relationships between these...
Source: http://arxiv.org/abs/hep-th/9703209v1
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Sep 19, 2013
09/13
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Ian I. Kogan; Alexei M. Tsvelik
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We show that $SL(2;C)/SU(2)$ model which had been recently proposed to describe the behaviour of the local densities of states at the plateau transition in Integer Quantum Hall effect, has logarithmic operators. They unusual properties are studied in this letter.
Source: http://arxiv.org/abs/hep-th/9912143v1
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Sep 21, 2013
09/13
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William E. Brown; Ian I. Kogan
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The beta-function is calculated for an SU(N) Yang-Mills theory from an ansatz for the vacuum wavefunctional. Direct comparison is made with the results of calculations of the beta-function of QCD. In both cases the theories are asymptotically free. The only difference being in the numerical coefficient of the beta-function, which is found to be -4 from the ansatz and -4+1/3 from other QCD calculations. This is because, due to the constraint of Gauss' law applied to the wavefunctional,...
Source: http://arxiv.org/abs/hep-th/9705136v2
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Jul 20, 2013
07/13
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R. D. Amado; Ian I. Kogan
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We consider the quantum state describing theDisoriented Chiral Condensate (DCC), which may be produced in high energy collisions. We show how a mean field treatment of the quantum equations corresponding to the classical linear sigma model leads to a squeezed state description of the pions emerging from the DCC. We examine various squeezed and coherent state descriptions of those pions with particular attention to charge and number fluctuations. We also study the phenomenology of multiple DCC...
Source: http://arxiv.org/abs/hep-ph/9407252v1
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Sep 23, 2013
09/13
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Ian I. Kogan; Nick E. Mavromatos
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We discuss the target-space interpretation of the world-sheet logarithmic operators in string theory. These operators generate the normalizable zero modes (discrete states) in target space, which restore the symmetries of the theory broken by the background. The problem of the recoil in string theory is considered, as well as some general properties of string amplitudes containing logarithmic operators.
Source: http://arxiv.org/abs/hep-th/9512210v2
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Sep 18, 2013
09/13
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Ian I. Kogan; Alex Kovner; Bayram Tekin
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We show that correlators of some local operators in gauge theories are sensitive to the presence of the instantons even at high temperature where the latter are bound into instanton-anti-instanton "molecules". We calculate correlation functions of such operators in the deconfined phase of the 2+1 dimensional Georgi-Glashow model and discuss analogous quantities in the chirally symmetric phase of QCD. We clarify the mechanism by which the instanton-anti-instanton molecules contribute...
Source: http://arxiv.org/abs/hep-th/0101171v2
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Sep 22, 2013
09/13
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Ian I. Kogan; Martin Schvellinger; Bayram Tekin
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We study the Renormalization Group (RG) flow of critical bosonic background fields in the framework of the RG approach to string theory. In this approach quantum field theory beta-functions are the extra inputs in solving the string theory sigma-model equations. We study two different situations, the first one is the Yang-Mills theory where the coupling constant diverges in the infrared limit. The second case corresponds to a type of theories where the beta-function has a pole in the infrared...
Source: http://arxiv.org/abs/hep-th/0004185v2
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Jul 20, 2013
07/13
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Ian I. Kogan; Alex Kovner; Mikhail Shifman
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Various features of domain walls in supersymmetric gluodynamics are discussed. We give a simple field-theoretic interpretation of the phenomenon of strings ending on the walls recently conjectured by Witten. An explanation of this phenomenon in the framework of gauge field theory is outlined. The phenomenon is argued to be particularly natural in supersymmetric theories which support degenerate vacuum states with distinct physical properties. The issue of existence (or non-existence) of the BPS...
Source: http://arxiv.org/abs/hep-th/9712046v2
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Sep 18, 2013
09/13
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Thibault Damour; Ian I. Kogan; Antonios Papazoglou
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We explore spherically symmetric stationary solutions, generated by ``stars'' with regular interiors, in purely massive gravity. We reexamine the claim that the resummation of non-linear effects can cure, in a domain near the source, the discontinuity exhibited by the linearized theory as the mass m of the graviton tends to zero. First, we find analytical difficulties with this claim, which appears not to be robust under slight changes in the form of the mass term. Second, by numerically...
Source: http://arxiv.org/abs/hep-th/0212155v2
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Sep 18, 2013
09/13
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Steven Abel; Katherine Freese; Ian I. Kogan
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We examine the cosmological effects of the Hagedorn phase in models where the observable universe is pictured as a D-brane. It is shown that, even in the absence of a cosmological constant, winding modes cause a negative `pressure' that can drive brane inflation of various types including both power law and exponential. We also find regimes in which the cosmology is stable but oscillating (a bouncing universe) with the Hagedorn phase softening the singular behavior associated with the collapse.
Source: http://arxiv.org/abs/hep-th/0005028v1
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Sep 21, 2013
09/13
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Ian. I Kogan; Alex Kovner; Bayram Tekin
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We analyse the deconfining phase transition in the SU(N) Georgi-Glashow model in 2+1 dimensions. We show that the phase transition is second order for any N, and the universality class is different from the Z(N) invariant Villain model. At large N the conformal theory describing the fixed point is a deformed SU(N)_1 WZNW model which has N-1 massless fields. It is therefore likely that its self-dual infrared fixed point is described by the Fateev-Zamolodchikov theory of Z(N) parafermions.
Source: http://arxiv.org/abs/hep-th/0104047v1
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Sep 22, 2013
09/13
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Ian I. Kogan; Stavros Mouslopoulos; Antonios Papazoglou
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We show that, by considering physics in dS_4 or AdS_4 spacetime, one can circumvent the van Dam - Veltman - Zakharov theorem which requires that the extra polarization states of a massive graviton do not decouple in the massless limit. It is shown that the smoothness of the m->0 limit is ensured if the H (``Hubble'') parameter, associated with the horizon of the dS_4 or AdS_4 space, tends to zero slower than the mass of the graviton m.
Source: http://arxiv.org/abs/hep-th/0011138v3
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Jul 20, 2013
07/13
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Ian I. Kogan; Nuno B. B. Reis
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We add a simple boundary term to the Polyakov action and construct a new class of D-branes with a single null direction. On the string world-sheet the system is described by a single quantized left-mode sector of a conformal field theory. By a Wick rotation of spacetime, we map open strings attached to these branes into chiral closed strings. We suggest that these so-called H-branes describe quantum horizons - black hole, cosmological (de-Sitter), etc. We show how one can get a space/phase...
Source: http://arxiv.org/abs/hep-th/0107163v1
