Superconformal surfaces in four dimensions

TL;DR

This paper explores the constraints of superconformal symmetry on four-dimensional defects, revealing relations between key physical quantities, and investigates the associated chiral algebra structures for supersymmetric surface defects.

Contribution

It establishes new relations between stress tensor one-point functions and displacement operator two-point functions, and analyzes the chiral algebra modules associated with supersymmetric surface defects.

Findings

Relation between stress tensor and displacement operator functions.

Proposed general relation for supersymmetric defects of various dimensions.

Explicit examples illustrating the chiral algebra properties of defects.

Abstract

We study the constraints of superconformal symmetry on codimension two defects in four-dimensional superconformal field theories. We show that the one-point function of the stress tensor and the two-point function of the displacement operator are related, and we discuss the consequences of this relation for the Weyl anomaly coefficients as well as in a few examples, including the supersymmetric R\'enyi entropy. Imposing consistency with existing results, we propose a general relation that could hold for sufficiently supersymmetric defects of arbitrary dimension and codimension. Turning to $\mathcal{N}=(2,2)$ surface defects in $\mathcal{N} \geqslant 2$ superconformal field theories, we study the associated chiral algebra. We work out various properties of the modules introduced by the defect in the original chiral algebra. In particular, we find that the one-point function of the stress tensor controls the dimension of the defect identity in chiral algebra, providing a novel way to compute it, once the defect identity is identified. Studying a few examples, we show explicitly how these properties are realized.