Small volume expansion of almost supersymmetric large N theories

TL;DR

This paper investigates the small-volume behavior of non-supersymmetric orbifold and orientifold theories on a three-torus, testing their planar equivalence to supersymmetric models through one-loop effective potential analysis.

Contribution

It demonstrates that planar equivalence holds on average over moduli space but can be locally violated due to nonlinear effects, especially in orbifold models.

Findings

Planar equivalence preserved on average over moduli space.

Local violations of equivalence occur at specific points in moduli space.

Twisted sectors dominate low-energy dynamics in orbifold models.

Abstract

We consider the small-volume dynamics of nonsupersymmetric orbifold and orientifold field theories defined on a three-torus, in a test of the claimed planar equivalence between these models and appropriate supersymmetric ``parent models". We study one-loop effective potentials over the moduli space of flat connections and find that planar equivalence is preserved for suitable averages over the moduli space. On the other hand, strong nonlinear effects produce local violations of planar equivalence at special points of moduli space. In the case of orbifold models, these effects show that the "twisted" sector dominates the low-energy dynamics.