Two Phases of Supersymmetric Gluodynamics
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.
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arXiv subjects
Ian I. Kogan
Publications and source records attributed to Ian I. Kogan.
Matching Conditions and Duality in N=1 SUSY Gauge Theories in the Conformal Window
We discuss duality in $N=1$ SUSY gauge theories in Seiberg's conformal window, $(3N_c/2)<N_f<3N_c$. The 't Hooft consistency conditions -- the basic tool for establishing the infrared duality -- are considered taking into account higher order $α$ corrections. The conserved (anomaly free) $R$ current is built to all orders in $α$. Although this current contains all orders in $α$ the 't Hooft consistency conditions for this current are shown to be one-loop. This observation thus justifies Seiberg's matching procedure. We also briefly discuss the inequivalence of the ``electric" and ``magnetic" theories at short distances.
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The Two Phases of Topologically Massive Compact $U(1)$ Theory
The mean field like gauge invariant variational method formulated recently, is applied to a topologically massive QED in 3 dimensions. We find that the theory has a phase transition in the Chern Simons coefficient $n$. The phase transition is of the Berezinsky-Kosterlitz - Thouless type, and is triggered by the liberation of Polyakov monopoles, which for $n>8$ are tightly bound into pairs. In our Hamiltonian approach this is seen as a similar behaviour of the magnetic vortices, which are present in the ground state wave functional of the compact theory. For $n>8$, the low energy behavior of the theory is the same as in the noncompact case. For $n<8$ there are no propagating degrees of freedom on distance scales larger than the ultraviolet cutoff. The distinguishing property of the $n<8$ phase, is that the magnetic flux symmetry is spontaneoously broken.
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Black Hole Spectrum, Horison Quantization and All That
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.
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Compact QED$_3$ - a simple example of a variational calculation in a gauge theory
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.
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A variational approach to the QCD wave functional:Dynamical mass generation and confinement
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 $Λ_{QCD}$ by the following relation: $α_{QCD}(M)={π\over 4}{1\over N}$. Taking the one loop QCD $β$- function and $Λ_{QCD}=150 Mev$ we find (for N=3) the vacuum condensate ${α\over π} = 0.008 Gev^4$.
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Gravitationally Dressed Conformal Field Theory and Emergence of Logarithmic Operators
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 dressed operator product expansions. We also show some evidence that non-conformal but integrable models may remain integrable when coupled to gravity.
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Quantum Phenomenology for the Disoriented Chiral Condensate
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 domains.
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Area-preserving diffeomorphisms, W_{\infty} and $U_{q}(sl(2)) in Chern-Simons theory and Quantum Hall system
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.
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The Goldberger -- Treiman Relation, $g_A$ and $g_{πNN}$ at $T\neq 0$
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 $F_π$, $g_{A}(T)=g_{A}(0)(1-T^2/12F^2)$, while $g_{πNN}$ is temperature independent to this order. The baryon octet ${\cal D}$ and ${\cal F}$ couplings also behave as $F_π$ if only pions are massless in the pseudoscalar meson octet.
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Hot Gauge Theories and $Z_{N}$ Phases
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 Euclidean theory, they cannot be interpreted as physical domains in Minkowski space. The related problem is connected with the analysis of the high-temperature limit of the confining phase. Using the two-dimensional QCD with adjoint fermions as a toy model we shall demonstrate that in the light fermion limit in this theory there is no breaking of the $Z_{N}$ symmetry in the high-temperature limit and thus there are no $Z_{N}$ bubbles.
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Squeezed Quantum State of Disoriented Chiral Condensate
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.
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Two Dimensional Field Theory Description of Disoriented Chiral Condensate
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 one-dimensional DDC. Some possible phenomenological consequences are briefly discussed.
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The Spectrum of Topologically Massive Quantum Electrodynamics
We discuss the possibility for the spectrum of topologically massive quantum electrodynamics with spinor matter fields to contain unexpected and unusual stable particle excitations for certain values of the topological photon mass. The new field theoretical phenomena arising from this novel spectral structure are briefly discussed.
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Area Preserving Diffeomorphisms and $W_{\infty}$ Symmetry in a $2+1$ Chern-Simons Theory
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.
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About some exact solutions for 2+1 gravity coupled to gauge fields
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.
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