Holographic Operator Product Expansion of Loop Operators in $\mathcal{N}=4$ $SO(N)$ Super Yang-Mills Theory

In this paper, we compute the correlation functions of Wilson(-'t~Hooft) loops with chiral primary operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory with $SO(N)$ gauge symmetry, which has a holographic dual description of Type IIB superstring theory on the $AdS_{5}\times\mathbf{RP}^{5}$ background. Specifically, we compute the coefficients of the chiral primary operators in the operator product expansion of Wilson loops in the fundamental representation, Wilson-'t Hooft loops in the symmetric representation, Wilson loops in the anti-fundamental representation and the spinor representation. We also compare these results to the $\mathcal{N}=4$ $SU(N)$ super Yang-Mills theory.Comment: v2, 22 pages, no figures, comparing with results in the case of gauge group SU(N) added, other minor reversion performed; v1, 20 pages, no figure