Information theoretic inequalities as bounds in superconformal field theory

Abstract

In this paper, an information theoretic approach to bounds in superconformal field theories is proposed. It is proved that the supersymmetric Rényi entropy [Formula: see text] is a monotonically decreasing function of [Formula: see text] and [Formula: see text] is a concave function of [Formula: see text]. Under the assumption that the thermal entropy associated with the “replica trick” time circle is bounded from below by the charge at [Formula: see text], it is further proved that both [Formula: see text] and [Formula: see text] monotonically increase as functions of [Formula: see text]. Because [Formula: see text] 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 [Formula: see text]. Some of the bounds coincide with Hofman–Maldacena bounds and the others are new. We also check the inequalities for examples in odd-dimensions.