Moduli space of supersymmetric QCD in the Veneziano limit

Abstract

We study the moduli space of 4d N=1 supersymmetric QCD in the Veneziano limit using Hilbert series. In this limit, the numbers of colours and flavours are taken to be large with their ratio fixed. It is shown that the Hilbert series, which is a partition function of an ensemble of gauge invariant quantities parametrising the moduli space, can also be realised as a partition function of a system of interacting Coulomb gas in two dimensions. In the electrostatic equilibrium, exact and asymptotic analyses reveal that such a system exhibits two possible phases. Physical quantities, such as charge densities, free energies, and Hilbert series, associated with each phase, are computed explicitly and discussed in detail. We then demonstrate the existence of the third order phase transition in this system.

38 pages; v2: clarifications added, published version

References in corpus (16)

• Counting Gauge Invariants: the Plethystic Program
• Lectures on non-perturbative effects in large N gauge theories, matrix models and strings
• Les Houches lectures on matrix models and topological strings
• SQCD: A Geometric Apercu
• Phases of large $N$ vector Chern-Simons theories on $S^2\times S^1$
• A Study of U(N) Lattice Gauge Theory in 2-dimensions
• Phases of M2-brane Theories
• Partition Functions for Membrane Theories
• Counting BPS Operators in the Chiral Ring of N=2 Supersymmetric Gauge Theories or N=2 Braine Surgery
• A Thermodynamic Interpretation of Time for Rolling Tachyons
• Timelike Boundary Sine-Gordon Theory and Two-Component Plasma
• N-point functions in rolling tachyon background
• A Thermodynamic Interpretation of Time for Superstring Rolling Tachyons
• Electrostatics of Coulomb gas, lattice paths, and discrete polynuclear growth
• The energy-momentum tensor of perturbed tachyon matter
• High-energy asymptotics of D-brane decay amplitudes from Coulomb gas electrostatics

Cited by in corpus (5)

• Painlevé III${}^{\prime }$ and the Hankel Determinant Generated by a Singularly Perturbed Gaussian Weight
• Asymptotics of determinants of Hankel matrices via non-linear difference equations
• Exact equivalences and phase discrepancies between random matrix ensembles
• New Phase Transitions in Chern-Simons Matter Theory
• Singular linear statistics of the Laguerre Unitary Ensemble and Painlevé III (${\mathrm{P}}_{\mathrm{III}}$): Double scaling analysis