Information Theoretic Inequalities as Bounds in Superconformal Field Theory
An information theoretic approach to bounds in superconformal field theories is proposed. It is proved that the supersymmetric Rényi entropy $\bar S_α$ is a monotonically decreasing function of $α$ and $(α-1)\bar S_α$ is a concave function of $α$. Under the assumption that the thermal entropy associated with the "replica trick" time circle is bounded from below by the charge at $α\to\infty$, it is further proved that both ${α-1\over α}\bar S_α$ and $(α-1)\bar S_α$ monotonically increase as functions of $α$. Because $\bar S_α$ 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 $\bar S_α$. Some of the bounds coincide with Hofman-Maldacena bounds and the others are new. We also check the inequalities for examples in odd-dimensions.