Supersymmetric Renyi Entropy and Anomalies in Six-Dimensional (1,0) Superconformal Theories

TL;DR

This work derives a universal cubic-form for the supersymmetric Rényi entropy in six-dimensional (1,0) SCFTs, with coefficients that are linear in the ’t Hooft anomaly data α,β,γ,δ. It connects Sν to both the Weyl anomaly coefficients and the anomaly polynomial, and demonstrates consistency with free multiplets, large-N theories, and even-dim anomaly-based predictions. A central conjecture equates supersymmetric Rényi entropy with an equivariant integral of the anomaly polynomial, supported by explicit six- and four-dimensional checks. The results yield linear relations between c-type Weyl anomalies and ’t Hooft anomalies, and offer a unified framework linking entanglement, Casimir energy, and anomaly structures in diverse dimensions.

Abstract

A closed formula of the universal part of supersymmetric Rényi entropy $S_q$ for six-dimensional $(1,0)$ superconformal theories is proposed. Within our arguments, $S_q$ across a spherical entangling surface is a cubic polynomial of $ν=1/q$, with $4$ coefficients expressed as linear combinations of the 't Hooft anomaly coefficients for the $R$-symmetry and gravitational anomalies. As an application, we establish linear relations between the $c$-type Weyl anomalies and the 't Hooft anomaly coefficients. We make a conjecture relating the supersymmetric Rényi entropy to an equivariant integral of the anomaly polynomial in even dimensions and check it against known data in four dimensions and six dimensions.