Related papers: ABJM quantum spectral curve at twist 1: algorithmi…

We present a simple algebraic method for the analytic continuation of harmonic sums with integer real or purely imaginary indices near negative and positive integers. We provide a MATHEMATICA code for exact expansion of harmonic sums in a…

We have recently constructed a large class of open quantum spin chains which have quantum-algebra symmetry and which are integrable. We show here that these models can be exactly solved using a generalization of the analytical Bethe Ansatz…

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…

The spectrum of anomalous dimensions of twist sl(2) operators in N=4 SYM has an intriguing feature in low twist 2 or 3. The anomalous dimension of the lowest state, dual a folded string on AdS_5 X S^5, can be computed by Bethe Ansatz at 3,…

We study the large $N$ limit of some supersymmetric partition functions of the $\mathrm{U}(N)_{k}\times \mathrm{U}(N)_{-k}$ ABJM theory computed by supersymmetric localization. We conjecture an explicit expression, valid to all orders in…

Infinite series of the type Sum{n=1,infinity}(alpha/2)_n_2F_1(-n, b; gamma; y)/(n n!) are investigated. Closed-form sums are obtained for alpha a positive integer alpha=1,2,3, ... The limiting case of b --> infinity, after y is replaced…

We give a derivation of quantum spectral curve (QSC) - a finite set of Riemann-Hilbert equations for exact spectrum of planar N=4 SYM theory proposed in our recent paper Phys.Rev.Lett. 112 (2014). We also generalize this construction to all…

We construct higher order spectral shift functions, extending the perturbation theory results of M. G. Krein and L. S. Koplienko on representations for the remainders of the first and second order Taylor-type approximations of operator…

In this short note we begin the analysis of deformed integrable Chern-Simons theories. We construct the two loop dilatation operator for the scalar sector of the ABJM theory with $k1 \neq -k2$ and we compute the anomalous dimension of some…

We study the spectrum of anomalous dimensions of short operators in planar ABJM theory at two loops. Specifically we develop a method for solving the OSp(6|4) Bethe ansatz equations for a certain class of unpaired length-4 states with…

In integrable spin chains, the spectral problem can be solved by the method of Bethe ansatz, which transforms the problem of diagonalization of the Hamiltonian into the problem of solving a set of algebraic equations named Bethe equations.…

We study the mixing problem of the determinant like operators in ABJM theory to two loop order in the scalar sector. The gravity duals of these operators are open strings attached to the maximal giant graviton, which is a D4-brane wrapping…

We introduce a method to obtain the analytic solution of the higher-order Baxter equation for twist-two and twist-three operators of planar N=4 SYM. Our result proofs the conjectured formula for the three-loop anomalous dimension of…

Recently, several multi-loop conjectures have been proposed for the spin dependence of anomalous dimensions of twist-2 and 3 operators in the sl(2) sector of N=4 SYM. Currently, these conjectures are not proven, although several consistency…

We propose a definition for a Tau function and a spinor kernel (closely related to Baker-Akhiezer functions), where times parametrize slow (of order 1/N) deformations of an algebraic plane curve. This definition consists of a formal…

The spectrum of anomalous dimensions of gauge-invariant operators in maximally supersymmetric Yang-Mills theory is believed to be described by a long-range integrable spin chain model. We focus in this study on its $sl(2)$ subsector spanned…

We develop powerful numerical and analytical techniques for the solution of the Helmholtz equation on general domains. We prove two theorems: the first theorem provides an exact formula for the ground state of an arbirtrary membrane, while…

We review the quantum spectral curve (QSC) formalism for anomalous dimensions of planar ${\cal\ N}=4$ SYM, including its $\gamma$-deformation. Leaving aside its derivation, we concentrate on formulation of the "final product" in its most…

As was recently found in hep-th/0304255, there exists a simple non-supersymmetric classical solution describing a closed string rotating in S^5 and located at the center of AdS_5. It is parametrized by the angular momentum J of the center…

Results of applying analytic perturbation theory (APT) to the Bjorken sum rule are presented. We study the third-order QCD correction within the analytic approach and investigate its renormalization scheme dependence. We demonstrate that,…