Holographic partition functions and phases for higher genus Riemann surfaces

Abstract

We describe a numerical method to compute the action of Euclidean saddlepoints for the partition function of a two-dimensional holographic CFT on a Riemann surface of arbitrary genus, with constant curvature metric. We explicitly evaluate the action for the saddles for genus two and map out the phase structure of dominant bulk saddles in a two-dimensional subspace of the moduli space. We discuss spontaneous breaking of discrete symmetries, and show that the handlebody bulk saddles always dominate over certain non-handlebody solutions.

27 pp + appendix

References in corpus (6)

• Three-Dimensional Gravity Revisited
• Entanglement Entropy at Large Central Charge
• The Holographic Entropy Cone
• The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT
• Poincare Series, 3D Gravity and CFT Spectroscopy
• Entanglement entropy in three dimensional gravity

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