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

We study the supersymmetric Wilson loops in the four-dimensional N = 4 super YangMills 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, Wk(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 SD3 for a probe D3-brane with k electric fluxes as 〈Wk(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 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. PACS codes: 11.15.Pg, 11.25.Tq, 11.25.Uv.