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

Abstract

Abstract We study the ’t Hooft expansion of d = 4 $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills (SYM) theory with the gauge group SO(N) or Sp(N). We consider the 1/N5 expansion with fixed gsN5, where gs denotes the string coupling of bulk type IIB string theory on AdS5×$$ \mathbbm{RP} $$ RP 5 and N5 refers to the RR 5-form flux through $$ \mathbbm{RP} $$ RP 5. N5 differs from N due to a shift coming from the RR charge of O3-plane. As an example, we consider the 1/N5 expansion of the free energy of $$ \mathcal{N} $$ N = 4 SYM on S4 and the 1/2 BPS circular Wilson loops in the fundamental representation of SO(N) or Sp(N). We find that the 1/N5 expansion is more “closed string like” than the ordinary 1/N expansion.