Supersymmetric Rényi Entropy in Two Dimensions

Abstract

We compute the exact partition function on the branched two-sphere by the localization technique. It is found that it does not depend on a branching parameter q, which means that supersymmetric Rényi entropy defined by utilizing it is equivalent to the usual entanglement entropy. We also provide the interpretation of the conical singularities on the branched sphere as defects sit on the poles of the nonsingular two-sphere.

27 pages; v2: typos and discussions revised, and reference added; v3: typos corrected and published in JHEP

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• Super Yang-Mills on Branched Covers and Weighted Projective Spaces
• Holographic supersymmetric Renyi entropies from hyperbolic black holes with scalar hair
• Information Theoretic Inequalities as Bounds in Superconformal Field Theory