Supersymmetric Renyi Entropy and Weyl Anomalies in Six-Dimensional (2,0) Theories

Abstract

We propose a closed formula of the universal part of supersymmetric Rényi entropy $S_q$ for $(2,0)$ superconformal theories in six-dimensions. We show that $S_q$ across a spherical entangling surface is a cubic polynomial of $\gamma :=1/q$, with all coefficients expressed in terms of the newly discovered Weyl anomalies $a$ and $c$. This is equivalent to a similar statement of the supersymmetric free energy on conic (or squashed) six-sphere. We first obtain the closed formula by promoting the free tensor multiplet result and then provide an independent derivation by assuming that $S_q$ can be written as a linear combination of 't Hooft anomaly coefficients. We discuss a possible lower bound $\frac{a}{c}\ge \frac{3}{7}$ implied by our result.

30 pages+1 table

References in corpus (22)

• Towards a derivation of holographic entanglement entropy
• Conformal collider physics: Energy and charge correlations
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• Four-Dimensional SCFTs from M5-Branes
• M5-Branes, D4-Branes and Quantum 5D super-Yang-Mills
• On D=5 super Yang-Mills theory and (2,0) theory
• Anomaly polynomial of general 6d SCFTs
• Localization on Hopf surfaces
• Instantons on the 5-sphere and M5-branes
• A Non-Abelian Self-Dual Gauge Theory in 5+1 Dimensions
• From Rigid Supersymmetry to Twisted Holomorphic Theories
• Superconformal Partition Functions and Non-perturbative Topological Strings
• Exact and Numerical Results on Entanglement Entropy in (5+1)-Dimensional CFT
• Supersymmetric Rényi Entropy in Five Dimensions
• Renyi entropy, stationarity, and entanglement of the conformal scalar
• Super-Rényi Entropy & Wilson Loops for N=4 SYM and their Gravity Duals
• N = 4 Super-Yang-Mills on Conic Space as Hologram of STU Topological Black Hole
• The holographic supersymmetric Renyi entropy in five dimensions
• Higher Derivative Terms, Toroidal Compactification, and Weyl Anomalies in Six-Dimensional (2,0) Theories
• Supersymmetric Renyi Entropy in $CF{T}_2$ and $Ad{S}_3$
• Rigid Holography and Six-Dimensional N=(2,0) Theories on AdS_5 times S^1
• Renyi Entropy of Free (2,0) Tensor Multiplet and its Supersymmetric Counterpart

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