12 loops and triple wrapping in ABJM theory from integrability

TL;DR

This paper develops a systematic algorithm using the Quantum Spectral Curve to compute high-order weak coupling expansions of anomalous dimensions in planar ABJM theory, achieving explicit results up to 12 loops and validating with TBA data.

Contribution

It introduces a novel method for calculating high-loop anomalous dimensions in ABJM theory using integrability and the Quantum Spectral Curve, extending beyond previous approaches.

Findings

Explicit 12-loop results for twist operators L=1,2

Agreement with Thermodynamic Bethe Ansatz data

Algorithm applicable to arbitrary orders and operators

Abstract

Adapting a method recently proposed by C. Marboe and D. Volin for ${\cal N}$=4 super-Yang-Mills, we develop an algorithm for a systematic weak coupling expansion of the spectrum of anomalous dimensions in the $sl(2)$-like sector of planar $\mathcal{N}$=6 super-Chern-Simons. The method relies on the Quantum Spectral Curve formulation of the problem and the expansion is written in terms of the interpolating function $h(\lambda)$, with coefficients expressible as combinations of Euler-Zagier sums with alternating signs. We present explicit results up to 12 loops (six nontrivial orders) for various twist L=1 and L=2 operators, corresponding to triple and double wrapping terms, respectively, which are beyond the reach of the Asymptotic Bethe Ansatz as well as L\"uscher's corrections. The algorithm works for generic values of L and S and in principle can be used to compute arbitrary orders of the weak coupling expansion. For the simplest operator with L=1 and spin S=1, the Pad\'e extrapolation of the 12-loop result nicely agrees with the available Thermodynamic Bethe Ansatz data in a relatively wide range of values of the coupling. A Mathematica notebook with a selection of results is attached.