Bootstrapping Monodromy Defects in the Wess-Zumino Model

TL;DR

This paper applies analytical bootstrap methods to study supersymmetric monodromy defects in the critical Wess-Zumino model, extending techniques for defects and bootstrap in the epsilon expansion to gain spectral insights.

Contribution

It introduces new analytical bootstrap techniques for supersymmetric monodromy defects and extends existing methods to accommodate parity-odd structures and defect-related correlators.

Findings

Derived explicit expressions for two-point functions with defects

Extended conformal block and inversion formula techniques to include parity-odd structures

Provided spectral data for the bulk Wess-Zumino model in epsilon expansion

Abstract

We use analytical bootstrap techniques to study supersymmetric monodromy defects in the critical Wess-Zumino model. In preparation for this result we first study two related systems which are interesting on their own: general monodromy defects (no susy), and the $\varepsilon$--expansion bootstrap for the Wess-Zumino model (no defects). For general monodromy defects, we extend previous work on codimension-two conformal blocks and the Lorentzian inversion formula in order to accommodate parity-odd structures. In the Wess-Zumino model, we bootstrap four-point functions of chiral operators in the $\varepsilon$--expansion, with the goal of obtaining spectral information about the bulk theory. We then proceed to bootstrap two-point functions of chiral operators in the presence of a monodromy defect, and obtain explicit expressions in terms of novel special functions which we analyze in detail. Several of the results presented in this paper are quite general and should be applicable to other setups.