Deformations of surface defect moduli spaces

TL;DR

This paper investigates how marginal perturbations in 4d ${ m N}=2$ theories induce complex structure deformations in surface defect moduli spaces, using bulk-defect OPE for computation.

Contribution

It provides a concrete method to compute complex structure deformations of defect moduli spaces via bulk-defect OPE in supersymmetric theories.

Findings

Derived a formula relating bulk perturbations to defect moduli space deformations.

Established a computational approach for complex structure changes in defect moduli spaces.

Linked bulk theory perturbations to geometric deformations of surface defects.

Abstract

Given a 4d ${\mathcal N}=2$ supersymmetric theory with an ${\mathcal N}=(2,2)$ supersymmetric surface defect, a marginal perturbation of the bulk theory induces a complex structure deformation of the defect moduli space. We describe a concrete way of computing this deformation using the bulk-defect OPE.