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Journal of High Energy Physics

, 2019:18 | Cite as

ABJM quantum spectral curve at twist 1: algorithmic perturbative solution

  • R.N. Lee
  • A.I. OnishchenkaEmail author
Open Access
Regular Article - Theoretical Physics
  • 16 Downloads

Abstract

We present an algorithmic perturbative solution of ABJM quantum spectral curve at twist 1 in sl (2) sector for arbitrary spin values, which can be applied to, in principle, arbitrary order of perturbation theory. We determined the class of functions- products of rational functions in spectral parameter with sums of Baxter polynomials and Hurwitz functions - closed under elementary operations, such as shifts and partial fractions, as well as differentiation. It turns out, that this class of functions is also sufficient for finding solutions of inhomogeneous Baxter equations involved. For the latter purpose we present recursive construction of the dictionary for the solutions of Baxter equations for given inhomogeneous parts. As an application of the proposed method we present the computation of anomalous dimensions of twist 1 operators at six loop order. There is still a room for improvements of the proposed algorithm related to the simplifications of arising sums. The advanced techniques for their reduction to the basis of generalized harmonic sums will be the subject of subsequent paper. We expect this method to be generalizable to higher twists as well as to other theories, such as \( \mathcal{N} \) = 4 SYM.

Keywords

AdS-CFT Correspondence Chern-Simons Theories IntegTable Field Theories Supersymmetric Gauge Theory 

Notes

Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Budker Institute of Nuclear PhysicsNovosibirskRussia
  2. 2.Bogoliubov Laboratory of Theoretical PhysicsJoint Institute for Nuclear ResearchDubnaRussia
  3. 3.Mosccrw Institute of Physics and Technology (State University)DolgoprudnyRussia
  4. 4.Skobeltsyn Institute of Nuclear PhysicsMoscow State UniversityMoscowRussia

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