Information Theoretic Inequalities as Bounds in Superconformal Field Theory

Abstract

An information theoretic approach to bounds in superconformal field theories is proposed. It is proved that the supersymmetric Rényi 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 $\frac{\alpha -1}{\alpha }{\bar{S}}_{\alpha }$ 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.

8 pages, v2: one reference added+minor changes+assumption relaxed

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