Toward Precision Holography in Type IIA with Wilson Loops

Abstract

We study the one-loop effective action of certain classical type IIA string configurations in $Ad{S}_4\times {\mathbb{CP}}^3$. These configurations are dual to Wilson loops in the $\mathcal{N}=6$ $U(N{)}_k\times U(N{)}_{-k}$ 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 $\zeta$-function regularization. We find that the result of the perturbative heat kernel method matches the field theory prediction at the appropriate order while the $\zeta$-function approach seems to lead to a disagreement. We explore various issues that might be responsible for this state of affairs.

48 pages. v2: references added