Large $N$ Phases of Chiral QCD_2

Abstract

A matrix model is constructed which describes a chiral version of the large $N$ $U(N)$ gauge theory on a two-dimensional sphere of area $A$. This theory has three separate phases. The large area phase describes the associated chiral string theory. An exact expression for the free energy in the large area phase is used to derive a remarkably simple formula for the number of topologically inequivalent covering maps of a sphere with fixed branch points and degree $n$.

24 pgs., with 4 (postscript) figures included. MIT-CTP-2303

References in corpus (12)

• Two Dimensional QCD is a String Theory
• Large $N$ Phase Transition in Continuum QCD${}_2$
• Two Dimensional QCD as a String Theory
• Twists and Wilson Loops in the String Theory of Two Dimensional QCD
• Large N 2D Yang-Mills Theory and Topological String Theory
• Classical Solutions for Two Dimensional QCD on the Sphere
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• Large-N quantum gauge theories in two dimensions
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Cited by in corpus (25)

• Hurwitz numbers and intersections on moduli spaces of curves
• From Matrix Models and quantum fields to Hurwitz space and the absolute Galois group
• Phase transitions, double-scaling limit, and topological strings
• Topological strings and large N phase transitions II: Chiral expansion of q-deformed Yang-Mills theory
• Phase transitions in q-deformed 2d Yang-Mills theory and topological strings
• Nonperturbative Effects and the Large-Order Behavior of Matrix Models and Topological Strings
• Interacting systems and wormholes
• On Hurwitz numbers and Hodge integrals
• Holomorphic maps and the complete 1/N expansion of 2D SU(N) Yang-Mills
• Wilson Loops in 2D Yang Mills: Euler characters and Loop equations
• Large $N$ phase transition in $T\overline{T}$-deformed $2d$ Yang-Mills theory on the sphere
• All orders asymptotic expansion of large partitions
• The number of ramified covering of a Riemann surface by Riemann surface
• Black-holes, topological strings and large N phase transitions
• Enumerative geometry of plane curves of low genus
• Uniqueness of the minimum of the free energy of the 2D Yang-Mills theory at large N
• Two-dimensional gauge theories of the symmetric group S_n in the large-n limit
• Mirror symmetry for extended affine Weyl groups
• Large-N Universality of the Two-Dimensional Yang-Mills String
• Universal Aspects of Two-Dimensional Yang-Mills Theory at Large N
• The Master Field For 2D QCD On The Sphere
• A Formula about W-operator and Its Application to Hurwitz Number
• W-Operator and Differential Equation for 3-Hurwitz Number
• Non-local 2D Generalized Yang-Mills theories on arbitrary surfaces with boundary
• Minimal degree rational open up mappings and related questions