Information Theoretic Inequalities as Bounds in Superconformal Field Theory

TL;DR

This paper introduces an information theoretic framework to derive bounds on superconformal field theories using supersymmetric R'enyi entropy, establishing new inequalities related to Weyl anomaly coefficients and confirming them in various dimensions.

Contribution

It develops a novel information theoretic approach to bounding superconformal field theories and derives new inequalities for Weyl anomaly coefficients based on R'enyi entropy properties.

Findings

Proves monotonicity and concavity of supersymmetric R'enyi entropy.

Derives bounds on Weyl anomaly coefficients from entropy inequalities.

Validates inequalities in odd-dimensional examples.

Abstract

An information theoretic approach to bounds in superconformal field theories is proposed. It is proved that the supersymmetric R\'enyi entropy $\bar S_\alpha$ is a monotonically decreasing function of $\alpha$ and $(\alpha-1)\bar S_\alpha$ is a concave function of $\alpha$. Under the assumption that the thermal entropy associated with the "replica trick" time circle is bounded from below by the charge at $\alpha\to\infty$, it is further proved that both ${\alpha-1\over \alpha}\bar S_\alpha$ and $(\alpha-1)\bar S_\alpha$ monotonically increase as functions of $\alpha$. Because $\bar S_\alpha$ enjoys universal relations with the Weyl anomaly coefficients in even-dimensional superconformal field theories, one therefore obtains a set of bounds on these coefficients by imposing the inequalities of $\bar S_\alpha$. Some of the bounds coincide with Hofman-Maldacena bounds and the others are new. We also check the inequalities for examples in odd-dimensions.