Massive Orbifold

TL;DR

This paper investigates 2d supersymmetric sigma models on orbifolds, revealing that massive orbifolds resolve singularities similarly to conformal ones and connecting their operator product expansions to solutions of nonlinear differential equations.

Contribution

It demonstrates that massive orbifolds have non-singular operator products and links their UV behavior to conformal operator product expansions, extending understanding beyond conformal theories.

Findings

Operator products of twist operators are non-singular in massive orbifolds.

Massive orbifolds' correlation functions recover conformal OPEs in the UV limit.

Conditions for non-singular solutions to nonlinear equations are derived from twist operator OPEs.

Abstract

We study some aspects of 2d supersymmetric sigma models on orbifolds. It turns out that independently of whether the 2d QFT is conformal the operator products of twist operators are non-singular, suggesting that massive (non-conformal) orbifolds also `resolve singularities' just as in the conformal case. Moreover we recover the OPE of twist operators for conformal theories by considering the UV limit of the massive orbifold correlation functions. Alternatively, we can use the OPE of twist fields at the conformal point to derive conditions for the existence of non-singular solutions to special non-linear differential equations (such as Painleve III).