# Matching quantum string corrections and circular Wilson loops in $AdS_4 \times CP^3$

## TL;DR

This paper extends the computation of quantum string corrections to holographic Wilson loops in AdS4×CP3, demonstrating exact matching with field theory predictions and highlighting the importance of boundary conditions for massless fermions.

## Contribution

It provides the first detailed semiclassical string analysis of Wilson loops in AdS4×CP3, confirming field theory results and clarifying boundary condition effects.

## Key findings

- Exact matching of string corrections with field theory proposals
- Explicit evaluation of fluctuation determinants using phase shifts
- Recovery of localization results for trivial Wilson loops

## Abstract

Recent progresses in the computation of quantum string corrections to holographic Wilson loops are extended to the case of strings in $AdS_{4}\times CP^{3}$. For this, the ratio of 1/2-BPS circular and 1/6-BPS latitude fermionic Wilson loops in ABJM is considered at strong coupling by studying the corresponding semiclassical string partition functions. Explicit evaluation of fluctuation determinants using phaseshifts and diffeomorphism invariant regulators leads to exact matching with the recent field theory proposal. Key to this computation is the choice of boundary conditions for massless fermions. In the limit for which the latitude Wilson loop has a trivial expectation value, the long known localization result for the 1/2-BPS fermionic circular Wilson loop in ABJM is recovered.