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

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, W-k (C), is calculable by using a Gaussian matrix model. In the gravity side, the expectation value of the loop is conjectured to be given by the classical value of the action S-D3 for a probe D3-brane with k electric fluxes as < W-k(C)> = e(-SD3). 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. We see that the position of an eigenvalue appears as the gauge field plus the scalar field integrated over the boundary of the probe D3-brane. In the course of our analysis, we also clarify the boundary condition on the D3-brane in terms of the Wilson loop.