12 loops and triple wrapping in ABJM theory from integrability

Abstract

Adapting a method recently proposed by C. Marboe and D. Volin for $\mathcal{N}$=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 Lüscher'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 Padé 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.

31 pages, 1 figure. A Mathematica notebook with a selection of results is attached (please download the compressed file "Results.nb" listed under "Other formats"). v2: typos corrected; more precise checks of the results; an earlier incorrect version of the figure was replaced. Published in JHEP

References in corpus (7)

• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Wrapping interactions at strong coupling -- the giant magnon
• The AdS4/CFT3 algebraic curve
• The Quantum Spectral Curve of the ABJM theory
• Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories
• Asymptotic Bethe Ansatz on the GKP vacuum as a defect spin chain: scattering, particles and minimal area Wilson loops
• The 2-loop generalized scaling function from the BES/FRS equation

Cited by in corpus (1)

• Quantum Spectral Curve for a Cusped Wilson Line in N=4 SYM