Boundary condition for D-brane from Wilson loop, and gravitational interpretation of eigenvalue in matrix model in AdS/CFT correspondence

TL;DR

This paper explores the AdS/CFT correspondence by relating Wilson loop expectation values in N=4 super Yang-Mills theory to D3-brane actions in gravity, interpreting matrix model eigenvalues as fluxes on the brane and clarifying boundary conditions.

Contribution

It provides a gravitational interpretation of matrix model eigenvalues as fluxes on D3-branes and clarifies boundary conditions in the AdS/CFT context.

Findings

Eigenvalues correspond to integrated fluxes on D3-branes

Boundary conditions for D3-branes are clarified in Wilson loop context

Matrix model resolvent relates to probe D3-brane properties

Abstract

We study the supersymmetric Wilson loops in the four-dimensional N=4 super Yang-Mills theory in the context of AdS/CFT correspondence. In the gauge theory side, it is known that the expectation value of the Wilson loops of circular shape with winding number k is calculable by using a Gaussian matrix model. On the other hand, in the gravity side, it has been conjectured that the expectation value of the Wilson loop is given by the classical value of the action for a probe D3-brane with k electric fluxes. Given such correspondence, we pursue the interpretation of the matrix model eigenvalue density, or more precisely the resolvent, from the viewpoint of the probe D3-brane in the gravity side. We see that in the gravity side, the position of an eigenvalue appears as an integrated flux on the D3-brane. In the course of our analysis, we also clarify the boundary condition on the D3-brane in terms of the Wilson loop.