Emergent bubbling geometries in gauge theories with SU(2|4) symmetry

TL;DR

This paper demonstrates the correspondence between bubbling geometries in type IIA supergravity and specific gauge theory configurations with SU(2|4) symmetry, establishing a duality through integral equations and matrix models.

Contribution

It reveals the equivalence between gravity bubbling geometries and gauge theory matrix eigenvalue densities via integral equations and localization techniques.

Findings

Bubbling geometries correspond to electrostatic systems with disks.

Eigenvalue densities satisfy the same integral equations as charge densities.

The duality is established through matrix integral and electrostatic system analysis.

Abstract

We study the gauge/gravity duality between bubbling geometries in type IIA supergravity and gauge theories with SU(2|4) symmetry, which consist of N=4 super Yang-Mills on $R\times S^3/Z_k$, N=8 super Yang-Mills on $R\times S^2$ and the plane wave matrix model. We show that the geometries are realized as field configurations in the strong coupling region of the gauge theories. On the gravity side, the bubbling geometries can be mapped to electrostatic systems with conducting disks. We derive integral equations which determine the charge densities on the disks. On the gauge theory side, we obtain a matrix integral by applying the localization to a 1/4-BPS sector of the gauge theories. The eigenvalue densities of the matrix integral turn out to satisfy the same integral equations as the charge densities on the gravity side. Thus we find that these two objects are equivalent.