Bubbling wormholes and matrix models

TL;DR

This paper proposes a new class of holographic duals called 'bubbling wormholes' constructed from sums over gauge group representations, linking matrix models with novel geometries in AdS/CFT correspondence.

Contribution

It introduces bubbling wormhole geometries as holographic duals to sums over gauge group representations in super Yang-Mills theory, expanding the understanding of entangled states in holography.

Findings

Matrix model free energy analysis supports the bubbling wormhole interpretation.

Probe loops in these backgrounds reveal new insights into the geometry.

The geometries involve multiple intersecting four-spheres at the boundary.

Abstract

The thermofield double state entangles two copies of a CFT via a sum over energy eigenstates and is dual to the two-sided eternal black hole. We explore an analogous construction using sums over gauge group representations of half-BPS Wilson loops in multiple copies of $U(N)$ $\mathcal{N}=4$ super Yang-Mills. These sums act as delta function-like operators that correlate the eigenvalues of the corresponding half-BPS matrix models. We suggest that the holographic duals are ''bubbling wormhole'' geometries: multi-covers of AdS$_5$ $\times S^5$ whose conformal boundary consists of multiple four-spheres intersecting on a common circle. We analyze the matrix model free energy, discuss its bulk interpretation, and study probe loops in these backgrounds.