Two-loop cusp anomaly in ABJM at strong coupling

TL;DR

This paper calculates the two-loop cusp anomalous dimension in ABJM theory at strong coupling, providing a perturbative check for the integrability-based conjecture of the coupling function and supporting the UV-finiteness of the superstring in this background.

Contribution

It offers the first two-loop strong coupling computation of the cusp anomaly in ABJM, confirming the conjectured form of the integrable coupling function and supporting superstring quantum integrability.

Findings

Two-loop cusp anomalous dimension matches the conjectured strong coupling expansion of h(λ).

Provides evidence for UV-finiteness of the superstring in AdS4×CP3.

Supports quantum integrability of the Type IIA superstring in this background.

Abstract

We compute the null cusp anomalous dimension of ABJM theory at strong coupling up to two-loop order. This is done by evaluating corrections to the corresponding superstring partition function, weighted by the $AdS_4\times \mathbb{CP}^3$ action in AdS light-cone gauge. We compare our result, where we use an anomalous shift in the $AdS_4$ radius, with the cusp anomaly of $\mathcal{N}=4$ SYM, and extract the two-loop contribution to the non-trivial integrable coupling $h(\lambda)$ of ABJM theory. It coincides with the strong coupling expansion of the exact expression for $ h(\lambda)$ recently conjectured by Gromov and Sizov. Our work provides thus a non-trivial perturbative check for the latter, as well as evidence for two-loop UV-finiteness and quantum integrability of the Type IIA $AdS_4\times \mathbb{CP}^3$ superstring in this gauge.