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

Understand

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.