Bubbling wormholes and matrix models

A

bstract

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 )

= 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 × 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.