(2,2) Superconformal Bootstrap in Two Dimensions

TL;DR

This paper establishes a relation between superconformal blocks and Virasoro blocks in 2D N=2 theories, enabling numerical bounds on operator spectra and revealing connections to known models like Liouville and Landau-Ginzburg theories.

Contribution

It introduces a novel relation simplifying superconformal bootstrap analysis in 2D N=2 theories and applies semidefinite programming to derive spectral bounds.

Findings

Bounds on non-BPS spectral gaps depend on moduli and chiral ring coefficients.

Some bounds are saturated by free theories, N=2 Liouville, and Landau-Ginzburg models.

The relation simplifies the analysis of BPS four-point functions in superconformal theories.

Abstract

We find a simple relation between two-dimensional BPS N=2 superconformal blocks and bosonic Virasoro conformal blocks, which allows us to analyze the crossing equations for BPS 4-point functions in unitary (2,2) superconformal theories numerically with semidefinite programming. We constrain gaps in the non-BPS spectrum through the operator product expansion of BPS operators, in ways that depend on the moduli of exactly marginal deformations through chiral ring coefficients. In some cases, our bounds on the spectral gaps are observed to be saturated by free theories, by N=2 Liouville theory, and by certain Landau-Ginzburg models.