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**public sources and our publisher partners.**A bstractWe give a derivation of quantum spectral curve (QSC) — a finite set of Riemann-Hilbert equations for exact spectrum of planar N=4$$ \mathcal{N}=4 $$ SYM theory proposed in our recent paper… Expand

We present a new formalism, alternative to the old thermodynamic-Bethe-ansatz-like approach, for solution of the spectral problem of planar N=4 super Yang-Mills theory. It takes a concise form of a… Expand

A bstractUsing integrability and analyticity properties of the AdS5/CFT4 Y-system we reduce it to a finite set of nonlinear integral equations. The $ {{\mathbb{Z}}_4} $ symmetry of the underlying… Expand

A bstractWe propose an efficient grassmannian formalism for solution of bi-linear finite-difference Hirota equation (T-system) on T-shaped lattices related to the space of highest weight… Expand

We present a new formalism, alternative to the old TBA-like approach, for solution of the spectral problem of planar N = 4 SYM. It takes a concise form of a non-linear matrix Riemann-Hilbert problem… Expand

Using the discrete Hirota integrability we find the general solution of the full quantum Y-system for the spectrum of anomalous dimensions of operators in the planar AdS5/CFT4 correspondence in terms… Expand

Using recently proposed method of discrete Hirota dynamics for integrable (1 + 1)D quantum field theories on a finite space circle of length L we derive and test numerically a finite system of… Expand

We propose the operatorial Baxter’s TQ-relations in a general form of the operatorial Bäcklund flow describing the nesting process for the inhomogeneous rational gl(K|M) quantum (super)spin chains… Expand

A bstractFor an arbitrary generalized quantum integrable spin chain we introduce a “master T -operator” which represents a generating function for commuting quantum transfer matrices constructed by… Expand

This thesis is devoted to the study of integrable quantum systems such as spin chains, two-dimensional field theories and the AdS/CFT duality. This AdS/CFT duality is a conjecture, stated in the end… Expand