From Weyl Anomaly to Defect Supersymmetric R\'enyi Entropy and Casimir Energy

TL;DR

This paper derives explicit formulas for surface defect contributions to supersymmetric Rny entropy and Casimir energy in six-dimensional (2,0) theories, linking them to Weyl anomaly coefficients.

Contribution

It provides the first closed-form expressions for defect contributions to supersymmetric Rny entropy and Casimir energy in 6D (2,0) theories, revealing their dependence on Weyl anomaly coefficients.

Findings

Defect contribution to Rny entropy is linear in 1/n and proportional to 2b - d_2.

Defect contribution to Casimir energy simplifies to -d_2 in the chiral algebra limit.

Explicit formulas connect defect contributions to Weyl anomaly coefficients.

Abstract

We present a closed-form expression for the contribution of surface defects to the supersymmetric R\'enyi entropy in six-dimensional $(2,0)$ theories. Our results show that this defect contribution is a linear function of $1/n$ and is directly proportional to $2b-d_2$, where $b$ and $d_2$ are the surface defect Weyl anomaly coefficients. We also derive a closed-form expression for the defect contribution to the supersymmetric Casimir energy, which simplifies to $-d_2$ (up to a proportionality constant) in the chiral algebra limit.