Toward Precision Holography in Type IIA with Wilson Loops

TL;DR

This paper compares two methods for calculating one-loop effective actions of string configurations in AdS4×CP3, finding agreement with field theory predictions for heat kernel but discrepancies with zeta-function regularization.

Contribution

It provides a detailed comparison of heat kernel and zeta-function techniques in holographic computations, highlighting their consistency and discrepancies.

Findings

Heat kernel method matches field theory predictions.

Zeta-function regularization shows discrepancies.

Discussion of potential reasons for differences.

Abstract

We study the one-loop effective action of certain classical type IIA string configurations in $AdS_4\times \mathbb{CP}^3$. 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.