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.
Highlights
ABJM quantum spectral curveAs it was already mentioned in introduction, the ABJM model is the second most popular playground for testing AdS/CFT correspondence
A detailed study of Thermodynamic Bethe Ansatz (TBA) equations for super spin chains corresponding to N = 4 SYM and ABJM models has led to their simplified alternative formulations in terms of Quantum Spectral Curve (QSC), a set of algebraic relations for Baxter type Q-functions together with analyticity and Riemann-Hilbert monodromy conditions for the latter [77,78,79,80,81,82,83,84]
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
Summary
As it was already mentioned in introduction, the ABJM model is the second most popular playground for testing AdS/CFT correspondence. In the present paper we will be interested in the calculation of anomalous dimensions of twist 1 gauge-invariant operators from sl(2) sector for arbitrary spin values S The latter are given by single-trace operators of the form [93]: tr D+S (Y 1Y4†)L. where twist 1 corresponds to L = 1. To perform actual calculations of anomalous dimensions we will use monodromy conditions for the part of ABJM Q-system known as Pνsystem [82, 83] The latter consists of six functions PA, A = 1, . The PA functions have a single cut on the defining Riemann sheet running from −2h to +2h (h is effective ABJM QSC coupling constant2), while νa, νa functions have an infinite set of branch cuts located at intervals (−2h, +2h) + in, n ∈ Z and satisfy simple quasi-periodicity relations νa(u) = eiP νa(u + i) , νa(u) = e−iP νa(u + i) ,.
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