Large N orbifold field theories on the twisted torus

TL;DR

This paper investigates the large N behavior of orbifold field theories on a twisted three-torus, revealing differences from supersymmetric models in moduli space, vacuum structure, and tunneling effects.

Contribution

It extends the analysis of orbifold theories to small twisted tori, highlighting non-supersymmetric dynamics and the lifting of zero modes compared to supersymmetric counterparts.

Findings

Nonsupersymmetric orbifold models differ in large N dynamics from supersymmetric ones.

A moduli space of zero modes is lifted by an $O(N^2)$ potential in daughter theories.

Discrepancies in vacuum counts and tunneling contributions are found due to fermionic zero modes.

Abstract

We study the planar equivalence of orbifold field theories on a small three-torus with twisted boundary conditions, generalizing the analysis of hep-th/0507267. The nonsupersymmetric orbifold models exhibit different large N dynamics from their supersymmetric "parent" counterparts. In particular, a moduli space of Abelian zero modes is lifted by an $O(N^2)$ potential in the "daughter" theories. We also find disagreement between the number of discrete vacua of both theories, due to fermionic zero modes in the parent theory, as well as the values of semiclassical tunneling contributions to fermionic correlation functions, induced by fractional instantons.