Twisted Massive Non-Compact Models

TL;DR

This paper investigates twisted massive non-compact N=(2,2) supersymmetric models derived from deformed conformal theories, providing explicit formulas for correlators, analyzing the topological sector, and revealing connections to affine Toda and Painlevé III equations.

Contribution

It introduces a detailed analysis of twisted non-compact models, deriving structure constants, correlators, and linking the metric to integrable differential equations like affine Toda and Painlevé III.

Findings

Determined structure constants of the chiral ring.

Provided formulas for deformed operators and solutions to WDVV equations.

Connected the metric to affine Toda and Painlevé III equations.

Abstract

We study interacting massive N=(2,2) supersymmetric field theories in two dimensions which arise from deforming conformal field theories with a continuous spectrum. Firstly, we deform N=2 superconformal Liouville theory with relevant operators, and twist the theory into a topological quantum field theory. These theories can be thought of as twisted Landau-Ginzburg models with negative power superpotential. We determine the structure constants of the chiral ring and therefore all correlators of these topological quantum field theories. We provide general formulas for the deformed operators of given charge as well as explicit solutions to the WDVV equations. Secondly, we analyze the topological anti-topological sector of the theory. We compute the metric at the conformal point through localization. Moreover, we show that the topological-anti-topological fusion differential equations on the metric in a family of non-compact theories takes the affine Toda form. The metric as a function of the family of theories is identical to the metric in certain deformed compact models. For a negative cubic power Landau-Ginzburg superpotential, for instance, it is governed by the Painlev\'e III differential equation.