One-loop corrections to holographic Wilson loop in AdS4xCP3

TL;DR

This paper computes one-loop quantum corrections to holographic Wilson loops in AdS4xCP3, advancing understanding of quantum effects in the AdS/CFT correspondence for N=6 Chern-Simons theory.

Contribution

It provides the first calculation of fermionic fluctuation modes and the one-loop effective action for Wilson loops in AdS4xCP3, highlighting the role of zero modes.

Findings

Fermionic mode frequencies expressed via hypergeometric functions

Numerical computation of the one-loop effective action

Discrepancy with localization due to zero mode normalization

Abstract

The evaluation of BPS Wilson loops in N=6, D=3 Chern-Simons matter theory is reduced to ordinary matrix integrals via localization technique. It is easy to check that the vacuum expectation value of 1/2 BPS Wilson loops at leading order in planar limit agrees with the regularized classical string action, via AdS/CFT. Then the subleading terms in principle can be calculated by treating the string theory semi-classically. In this article we calculate the one-loop determinant for fluctuation modes of holographic Wilson loop in the dual geometry AdS4xCP3. The fermionic normal mode frequencies are expressed in terms of the hypergeometric function, and we compute the one-loop effective action numerically. The discrepancy with localization formula is due to the zero mode normalization constant, which is yet to be determined.