Wilson loops in $\mathcal{N}=4$ $SO(N)$ SYM and D-Branes in $Ad{S}_5\times {\mathbb{RP}}^5$

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 $Ad{S}_5\times {\mathbb{RP}}^5$. 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 ${\mathbb{RP}}^4$ subspace of ${\mathbb{RP}}^5$. We also briefly discuss the large $N$, large $\lambda$ 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.

41 pages

References in corpus (8)

• Towards a derivation of holographic entanglement entropy
• Les Houches lectures on matrix models and topological strings
• Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
• Small deformations of supersymmetric Wilson loops and open spin-chains
• The 1/N correction in the D3-brane description of circular Wilson loop at strong coupling
• Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop
• Two universal results for Wilson loops at strong coupling
• Exact probes of orientifolds

Cited by in corpus (1)

• On disc-with-hole and disc-with-handle partition functions in bosonic string theory