# One-loop Holography with Strings in $AdS_4\times\mathbb {CP}^3$

## TL;DR

This paper calculates the one-loop quantum corrections to string configurations in $AdS_4\times\mathbb{CP}^3$ that correspond to latitude Wilson loops in ABJM theory, confirming the match with field theory results through localization.

## Contribution

It provides a detailed computation of one-loop determinants for string duals of latitude Wilson loops, including regularization and anomaly considerations, matching with supersymmetric localization results.

## Key findings

- One-loop determinants match field theory predictions.
- Regularization cancels divergences effectively.
- IR anomaly accounted for in the final result.

## Abstract

We compute the one-loop effective action of string configurations embedded in $AdS_4\times\mathbb{CP}^3$ which are dual to $\frac{1}{6}$-BPS latitude Wilson Loops in the ABJM theory. To avoid ambiguities in the string path integral we subtract the $\frac{1}{2}$-BPS case. The one-loop determinants are computed by Fourier-decomposing the two dimensional operators and then using the Gel'fand-Yaglom method. We comment on various aspects related to the regularization procedure, showing the cancellation of a hierarchy of divergences. After taking into account an IR anomaly from a change in topology, we find a precise agreement with the field theory result known from supersymmetric localization.