Quantum spectral curve as a tool for a perturbative quantum field theory

An iterative procedure perturbatively solving the quantum spectral curve of planar N=4 SYM for any operator in the sl(2) sector is presented. A Mathematica notebook executing this procedure is enclosed. The obtained results include 10-loop computations of the conformal dimensions of more than ten different operators. We prove that the conformal dimensions are always expressed, at any loop order, in terms of multiple zeta-values with coefficients from an algebraic number field determined by the one-loop Baxter equation. We observe that all the perturbative results that were computed explicitly are given in terms of a smaller algebra: single-valued multiple zeta-values times the algebraic numbers.Comment: 36 pages plus tables; v2: minor changes, references added, ancillary files with mathematica notebooks adde

Six-loop Konishi anomalous dimension from the Y-system

We compute the Konishi anomalous dimension perturbatively up to six loop using the finite set of functional equations derived recently by Gromov, Kazakov, Leurent and Volin. The recursive procedure can be in principle extended to higher loops, the only obstacle being the complexity of the computation.Comment: 5 pages, 1 figure, version 2 : published versio

Six-loop anomalous dimension of twist-two operators in planar N=4 SYM theory

We compute the general form of the six-loop anomalous dimension of twist-two operators with arbitrary spin in planar N=4 SYM theory. First we find the contribution from the asymptotic Bethe ansatz. Then we reconstruct the wrapping terms from the first 35 even spin values of the full six-loop anomalous dimension computed using the quantum spectral curve approach. The obtained anomalous dimension satisfies all known constraints coming from the BFKL equation, the generalised double-logarithmic equation, and the small spin expansion.Comment: 33 pages, 4 ancillary files, minor change

Bethe Algebra using Pure Spinors

We propose a gl(r)-covariant parameterisation of Bethe algebra appearing in so(2r) integrable models, demonstrate its geometric origin from a fused flag, and use it to compute the spectrum of periodic rational spin chains, for various choices of the rank r and Drinfeld polynomials.Comment: 9 pages of double-column text, Mathematica notebook attache

Monodromy Bootstrap for SU(2|2) Quantum Spectral Curves: From Hubbard model to AdS3/CFT2

We propose a procedure to derive quantum spectral curves of AdS/CFT type by requiring that a specially designed analytic continuation around the branch point results in an automorphism of the underlying algebraic structure. In this way we derive four new curves. Two are based on SU(2|2) symmetry, and we show that one of them, under the assumption of square root branch points, describes Hubbard model. Two more are based on SU(2|2) x SU(2|2). In the special subcase of zero central charge, they both reduce to the unique nontrivial curve which furthermore has analytic properties compatible with PSU(1,1|2) x PSU(1,1|2) real form. A natural conjecture follows that this is the quantum spectral curve of AdS/CFT integrable system with AdS3 x S3 x T4 background supported by RR-flux. We support the conjecture by verifying its consistency with the massive sector of asymptotic Bethe equations in the large volume regime. For this spectral curve, it is compulsory that branch points are not of the square root type which qualitatively distinguishes it from the previously known cases.Comment: 53 pages; substantial revisio