Abstract
We study the half-BPS circular Wilson loop in mathcal{N} = 4 super Yang-Mills with orthogonal gauge group. By supersymmetric localization, its expectation value can be computed exactly from a matrix integral over the Lie algebra of SO(N). We focus on the large N limit and present some simple quantitative tests of the duality with type IIB string theory in AdS5× ℝℙ5. In particular, we show that the strong coupling limit of the expectation value of the Wilson loop in the spinor representation of the gauge group precisely matches the classical action of the dual string theory object, which is expected to be a D5-brane wrapping a ℝℙ4 subspace of ℝℙ5. We also briefly discuss the large N, large λ limits of the SO(N) Wilson loop in the symmetric/antisymmetric representations and their D3/D5-brane duals. Finally, we use the D5-brane description to extract the leading strong coupling behavior of the “bremsstrahlung function” associated to a spinor probe charge, or equivalently the normalization of the two-point function of the displacement operator on the spinor Wilson loop, and obtain agreement with the localization prediction.
Highlights
We show that the strong coupling limit of the expectation value of the Wilson loop in the spinor representation of the gauge group precisely matches the classical action of the dual string theory object, which is expected to be a D5-brane wrapping a RP4 subspace of RP5
One can make contact with the dynamics of various stringy objects in the dual theory: while Wilson loops in the fundamental representation are described by string worldsheets, large representations with “size”2 of order N are dual to D-branes that pinch on the boundary contour [15,16,17], and even larger representations of order N 2 are dual to new supergravity backgrounds [18,19,20]
We studied the half-BPS circular Wilson loop in the N = 4 SYM theory with orthogonal gauge group
Summary
We have focused on the saddle point of SO(N ) in the even (i.e., N = 2N ) case, but the odd (i.e., N = 2N + 1) case yields a similar analysis and the same eigenvalue density distribution at large N. Implies that the expectation value of the SO(N ) Wilson loop in the fundamental representation is (choosing even N for simplicity, but the large N limit in the odd case is identical):. This is in precise agreement with eq (2.13) at leading order at large N. Up to a factor of 1/2 in the second term on the right hand side, this is the same as eq (2.27)
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