't Hooft expansion of $SO(N)$ and $Sp(N)$ $\mathcal{N}=4$ SYM revisited

Abstract

We study the 't Hooft expansion of $d=4$ $\mathcal{N}=4$ supersymmetric Yang-Mills (SYM) theory with the gauge group $SO(N)$ or $Sp(N)$. We consider the $1/N_5$ expansion with fixed $g_s{N}_5$, where $g_s$ denotes the string coupling of bulk type IIB string theory on $Ad{S}_5\times {\mathbb{RP}}^5$ and $N_5$ refers to the RR 5-form flux through ${\mathbb{RP}}^5$. $N_5$ differs from $N$ due to a shift coming from the RR charge of O3-plane. As an example, we consider the $1/N_5$ expansion of the free energy of $\mathcal{N}=4$ SYM on $S^4$ and the $1/2$ BPS circular Wilson loops in the fundamental representation of $SO(N)$ or $Sp(N)$. We find that the $1/N_5$ expansion is more "closed string like" than the ordinary $1/N$ expansion.

arXiv comment11 pages. v2: references added

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Cited by in corpus (1)

• $\mathcal{N}=4$ line defect correlators of type BCD