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

Understand

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.