Supersymmetric Warped Conformal Field Theory

TL;DR

This paper explores supersymmetric warped conformal field theories in two dimensions, extending symmetry enhancement theorems and analyzing their algebraic structures, states, and correlation functions.

Contribution

It generalizes the Hofman-Strominger theorem to supersymmetric cases and characterizes minimal models of supersymmetric warped conformal field theories.

Findings

Symmetry enhancement extends to supersymmetric theories.

Identifies two minimal models: N=(1,0) SCFT and N=1 SWCFT.

Analyzes representations, states, and superprimary correlations.

Abstract

In this work, we study the supersymmetric warped conformal field theory in two dimensions. We show that the Hofman-Strominger theorem on symmetry enhancement could be generalized to the supersymmetric case. More precisely, we find that within a chiral superspace $(x^+,\th)$, a two-dimensional field theory with two translational invariance and a chiral scaling symmetry can have enhanced local symmetry, under the assumption that the dilation spectrum is discrete and non-negative. Similar to the pure bosonic case, there are two kinds of minimal models, one being $N=(1,0)$ supersymmetric conformal field theories, while the other being $N=1$ supersymmetric warped conformal field theories (SWCFT). We study the properties of SWCFT, including the representations of the algebra, the space of states and the correlation functions of the superprimaries.