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

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.

40 pages, uses cite.sty; ver. 2, added references and footnotes

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Cited by in corpus (11)

• The 1/N correction in the D3-brane description of circular Wilson loop at strong coupling
• One-loop Structure of Higher Rank Wilson Loops in AdS/CFT
• Connected correlator of 1/2 BPS Wilson loops in $\mathcal{N}=4$ SYM
• On the structure of non-planar strong coupling corrections to correlators of BPS Wilson loops and chiral primary operators
• Spectral form factor and semi-circle law in the time direction
• Eigenvalue instantons in the spectral form factor of random matrix model
• Symmetric Wilson Loops beyond leading order
• One-point functions of non-SUSY operators at arbitrary genus in a matrix model for type IIA superstrings
• Wilson loop correlators in $\mathcal{N}=2$ superconformal quivers
• 't Hooft expansion of multi-boundary correlators in 2D topological gravity
• Loop equations for generalised eigenvalue models