One-loop Holography with Strings in $Ad{S}_4\times {\mathbb{CP}}^3$

Abstract

We compute the one-loop effective action of string configurations embedded in $Ad{S}_4\times {\mathbb{CP}}^3$ 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.

14 pages; v2: references added, comment about boundary conditions added