Hidden Symmetries of Large N QCD

The local SUSY symmetry of the loop dynamics of QCD is found. The remarkable thing is, there is no einbein-gravitino on this theory, which makes it a 1D topological supergravity, or locally SUSY quantum mechanics. Using this symmetry, we derive the large $N_c$ loop equation in momentum superloop space. Introducing as before the position operator \X{\mu} we argue that the superloop equation is equivalent to invariance of correlation functions of products of these operators with respect to certain quadrilinear transformation. The applications to meson and glueball sectors as well as the chiral symmetry breaking are discussed. The 1D field theory with Quark propagating around the loop in superspace is constructed.Comment: 40 pages, 1 Postscript figure, LaTe

From short to long scales in the QCD vacuum

We study approximate decimations in SU(N) LGT that connect the short to long distance regimes, and provide both upper and lower bounds on the exact partition function. This leads to a representation of the exact partition function in terms of successive decimations. The implications for a derivation of confinement from first principles are discussed.Comment: 3 pages, talk presented at Lattice2003(topology

Quark Confinement and the Renormalization Group

Recent approaches to quark confinement are reviewed, with an emphasis on their connection to renormalization group methods. Basic concepts related to confinement are introduced: the string tension, Wilson loops and Polyakov lines, string breaking, string tension scaling laws, center symmetry breaking, and the deconfinement transition at non-zero temperature. Current topics discussed include confinement on $R^3\times S^1$, the real-space renormalization group, the functional renormalization group, and the Schwinger-Dyson equation approach to confinement.Comment: 22 pages; report from the INT Workshop "New applications of the renormalization group in nuclear, particle, and condensed matter physics", held February 22-26 201

Mixed Model of Induced QCD

The problems with the $Z_N$ symmetry breaking in the induced QCD are analyzed. We compute the Wilson loops in the strong coupling phase, but we do not find the $Z_N$ symmetry breaking, for arbitrary potential. We suggest to bypass this problem by adding to the model a heavy fermion field in a fundamental representation of $SU(N)$. Remarkably, the model still can be solved exactly by the Rieman-Hilbert method, for arbitrary number $N_f$ of flavors. At $N_f \ll N \rightarrow \infty$ there is a new regime, with two vacuum densities. The $Z_N$ symmetry breaking density satisfies the linear integral equation, with the kernel, depending upon the old density. The symmetry breaking requires certain eigenvalue condition, which takes some extra parameter adjustment of the scalar potential.Comment: 14 pages, Latex, no figures, ( after final debugging

Bose Condensation and ZNZ_N Symmetry Breaking in the Mixed Model of Induced QCD

The mixed model of the large $N$ induced QCD, with $N_f \ll N$ flavors of heavy fermions in fundamental representation, is solved in the local limit. The $Z_N$ symmetry is broken spontaneously in the large $N$ limit, evading the Elitzur "no-go" theorem. As a result of this symmetry breaking, there is the Bose condensate of the eigenvalues of the scalar field, proportional to $\frac{N_f}{N}$. This condensate leads to the mass unit, which goes to zero as fractional power of $\frac{N_f}{N}$, thus defining the new kind of the local limit of this lattice theory. There is a strong coupling region below this mass scale, which revives the hopes of induction of realistic QCD.Comment: 16 pages, Latex, no figures, PUPT-134

1/N Expansion and Particle Spectrum in Induced QCD

We study the 1/N expansion in the recently proposed model of the lattice gauge theory induced by heavy scalar field in adjoint representation. In the first approximation the fluctuations of the density of eigenvalues of the scalar field are Gaussian, so that the scalar glueball spectrum is defined from the corresponding linear wave equation

Comment on Two Dimensional O(N) and Sp(N) Yang Mills Theories as String Theories

We write down all orders large $N$ expansions for the dimensions of irreducible representations of $O(N)$ and $Sp(N)$. We interpret all the terms in these expansions as symmetry factors for singular worldsheet configurations, involving collapsed crosscaps and tubes. We use it to complete the interpretation of two dimensional Yang Mills Theories with these gauge groups, on arbitrary two dimensional manifolds, in terms of a String Theory of maps of the type considered by Gross and Taylor. We point out some intriguing similarities to the case of $U(N)$ and discuss their implications.Comment: 18 pages (minor corrections made

Two-dimensional Born-Infeld gauge theory: spectrum, string picture and large-N phase transition

We analyze U(N) Born-Infeld gauge theory in two spacetime dimensions. We derive the exact energy spectrum on the circle and show that it reduces to N relativistic fermions on a dual space. This contrasts to the Yang-Mills case that reduces to nonrelativistic fermions. The theory admits a string theory interpretation, analogous to the one for ordinary Yang-Mills, but with higher order string interactions. We also demonstrate that the partition function on the sphere exhibits a large-N phase transition in the area and calculate the critical area. The limit in which the dimensionless coupling of the theory goes to zero corresponds to massless fermions, admits a perturbatively exact free string interpretation and exhibits no phase transition.Comment: 19 page