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

Yuhma Asano,Shinji Shimasaki,Goro Ishiki

doi:10.1007/jhep09(2014)137

Yuhma Asano, Shinji Shimasaki + Show 1 more

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https://doi.org/10.1007/jhep09(2014)137

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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 $$ \mathcal{N}=4 $$ super Yang-Mills on R × S 3/Z k , $$ \mathcal{N}=8 $$ super Yang-Mills on R × 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.

Highlights

One spatial direction in the dual ten-dimensional geometry
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 × S3/Zk, N = 8 super Yang-Mills on R × S2 and the plane wave matrix model
We showed that the bubbling geometries in type IIA supergravity are realized in the gauge theories with SU(2|4) symmetry

Summary

Lin-Maldacena solution

We review the Lin-Maldacena solution [13], which is the solution with SU(2|4) symmetry in type IIA supergravity. The electrostatic system relevant to PWMM consists of an infinite conducting plate at z = 0, some finite conducting disks in the region of z ≥ 0 (figure 1) and the background potential of the form. The electrostatic system relevant to N = 4 SYM on R × S3/Zk consists of an infinite number of finite conducting disks arranged periodically along the z-axis (figure 2 (right)) and the background potential (2.4).. We denote the total charge, the radius and the z-coordinate of s-th disk by Qs, Rs and ds, respectively, where s = 1, · · · , Λ In this case, there are Λ independent non-contractible S3’s and the same number of S6’s in the geometry.

Electrostatic problem for PWMM

Localization in PWMM

Correspondence to the gravity side

Summary

A Dual integral equations

C Condition for large S5 radius