Phase Transitions of Large N Orbifold Gauge Theories

TL;DR

This paper investigates the phase structure of large N orbifold gauge theories derived from N=4 super Yang-Mills, revealing phase transitions at zero coupling and exploring dualities with brane configurations and tachyon condensations.

Contribution

It provides a detailed analysis of phase transitions and dualities in large N orbifold gauge theories, including the computation of partition functions and the index for supersymmetric cases.

Findings

Phase transitions occur even at zero 't Hooft coupling.

Vacua are dual to arrangements of NS5-branes or tachyon condensations.

An index for the supersymmetric orbifold theory is obtained.

Abstract

We study the phase structures of N=4 U(N) super Yang-Mills theories on R x S^3/Z_k with large N. The theory has many vacua labelled by the holonomy matrix along the non-trivial cycle on S^3/Z_k, and for the fermions the periodic and the anti-periodic boundary conditions can be assigned along the cycle. We compute the partition functions of the orbifold theories and observe that phase transitions occur even in the zero 't Hooft coupling limit. With the periodic boundary condition, the vacua of the gauge theory are dual to various arrangements of k NS5-branes. With the anti-periodic boundary condition, transitions between the vacua are dual to localized tachyon condensations. In particular, the mass of a deformed geometry is compared with the Casimir energy for the dual vacuum. We also obtain an index for the supersymmetric orbifold theory.