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From Weyl Anomaly to Defect Supersymmetric Rényi Entropy and Casimir Energy

Zi-Xiao Huang, Ma-Ke Yuan, Yang Zhou

Abstract

We present a closed-form expression for the contribution of surface defects to the supersymmetric Rényi 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.

From Weyl Anomaly to Defect Supersymmetric Rényi Entropy and Casimir Energy

Abstract

We present a closed-form expression for the contribution of surface defects to the supersymmetric Rényi entropy in six-dimensional theories. Our results show that this defect contribution is a linear function of and is directly proportional to , where and 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 (up to a proportionality constant) in the chiral algebra limit.
Paper Structure (7 sections, 91 equations)

This paper contains 7 sections, 91 equations.

Table of Contents

  1. Anti-symmetric representation
  2. Superconformal algebra
  3. 6d bulk superconformal algebra
  4. With the 2d surface defect insertion
  5. Identifying the defect R-symmetry Cartans
  6. Equivariant integral of the anomaly polynomial
  7. Supersymmetric Entanglement entropy (SUSY EE) for Wilson loops in 4d