\begin{document}$ \mathcal{N}=4 $\end{document} supersymmetric Yang-Mills theory with \begin{document}$S O(N)$\end{document} gauge symmetry, which has a holographic dual description of the Type IIB superstring theory on the \begin{document}$ AdS_{5}\times\mathbf{RP}^{5} $\end{document} background. Specifically, we compute the coefficients of the chiral primary operators in the operator product expansion of Wilson loops in the fundamental representation, Wilson-'t Hooft loops in the symmetric representation, Wilson loops in the anti-fundamental representation, and Wilson loops in the spinor representation. We also compare these results to those of the \begin{document}$\mathcal{N}=4~ S U(N)$\end{document} super Yang-Mills theory."> Holographic operator product expansion of loop operators in the <inline-formula><tex-math id="M1">\begin{document}${{ \mathcal N} {\bf{=4}}\sim {\boldsymbol {S O(N)}}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/80eb43de-dcf1-4a9c-8dca-a384b4ca52a2/CPC-2023-0126_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/80eb43de-dcf1-4a9c-8dca-a384b4ca52a2/CPC-2023-0126_M1.png"/></alternatives></inline-formula> super Yang-Mills theory -
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