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We study the half-BPS circular Wilson loop in ${\cal N}=4$ super Yang-Millswith orthogonal gauge group. By supersymmetric localization, its expectationvalue 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 quantitativetests of the duality with type IIB string theory in $AdS_5\times\mathbb{RP}^5$. In particular, we show that the strong coupling limit of theexpectation value of the Wilson loop in the spinor representation of the gaugegroup 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 $\lambda$ limitsof the $SO(N)$ Wilson loop in the symmetric/antisymmetric representations andtheir D3/D5-brane duals. Finally, we use the D5-brane description to extractthe leading strong coupling behavior of the "bremsstrahlung function"associated to a spinor probe charge, or equivalently the normalization of thetwo-point function of the displacement operator on the spinor Wilson loop, andobtain agreement with the localization prediction.

Wilson loops in $\mathcal{N}=4$ $SO(N)$ SYM and D-Branes in $AdS_5\times \mathbb{RP}^5$