1/N expansion of the D3-D5 defect CFT at strong coupling

A bstract We consider four dimensional U( N ) N N = 4 SYM theory interacting with a 3d N N = 4 theory living on a codimension-one interface and holographically dual to the D3-D5 system without flux. Localization captures several observables in this dCFT, including its free energy, related to the defect expectation value, and single trace 1/2 1 2 -BPS composite scalars. These quantities may be computed in a hermitian one-matrix model with non-polynomial single-trace potential. We exploit the integrable Volterra hierarchy underlying the matrix model and systematically study its 1/ N expansion at any value of the ’t Hooft coupling. In particular, the strong coupling regime is determined — up to non-perturbative exponentially suppressed corrections — by differential relations that constrain higher order terms in the 1/ N expansion. The analysis is extended to the model with SU( N ) gauge symmetry by resorting to the more general Toda lattice equations.