Toward precision holography in type IIA with Wilson loops

Abstract

Abstract We study the one-loop effective action of certain classical type IIA string configurations in AdS4 × ℂℙ3. These configurations are dual to Wilson loops in the $$ \mathcal{N}=6 $$ N = 6 U(N) k × U(N)−k Chern-Simons theory coupled to matter whose expectation values are known via supersymmetric localization. We compute the one-loop effective actions using two methods: perturbative heat kernel techniques and full ζ-function regularization. We find that the result of the perturbative heat kernel method matches the field theory prediction at the appropriate order while the ζ-function approach seems to lead to a disagreement.