Holographic partition functions and phases for higher genus Riemann surfaces

TL;DR

This paper introduces a numerical method to compute holographic partition functions on higher genus Riemann surfaces, revealing phase structures and symmetry breaking in the bulk saddle solutions.

Contribution

It provides a new numerical approach for evaluating Euclidean saddlepoints and analyzes the phase dominance of handlebody solutions over non-handlebody ones.

Findings

Handlebody saddles dominate over non-handlebody solutions.

Explicit computation for genus two surfaces.

Spontaneous discrete symmetry breaking observed.

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.