T-and Y-systems are ubiquitous structures in classical and quantum integrable systems.
They are difference equations having a variety of aspects related to commuting transfer …

We review recent progress in understanding the notion of locality in integrable quantum
lattice systems. The central concept concerns the so-called quasilocal conserved quantities …

We review the quantum spectral curve (QSC) formalism for the spectrum of anomalous
dimensions of 𝒩= 4 SYM, including its γ-deformation. Leaving aside its derivation, we …

Anomalous finite-temperature transport has recently been observed in numerical studies of
various integrable models in one dimension; these models share the feature of being …

A bstract We give a derivation of quantum spectral curve (QSC)—a finite set of Riemann-
Hilbert equations for exact spectrum of planar\(\mathcal {N}= 4\) SYM theory proposed in our …

We present a set of functional equations defining the anomalous dimensions of arbitrary
local single trace operators in planar N= 4 supersymmetric Yang-Mills theory. It takes the …

We study the anomalous dimensions for scalar operators for a three-dimensional Chern-
Simons theory recently proposed in arXiv: 0806.1218. We show that the mixing matrix at two …

Using the thermodynamic Bethe ansatz method we derive an infinite set of integral non-
linear equations for the spectrum of states/operators in AdS/CFT. The Y-system conjectured …

A bstract We derive a set of integral equations of the TBA type for the generalized cusp
anomalous dimension, or the quark antiquark potential on the three sphere, as a function of …

The study of finite J effects for the light-cone AdS 5× S 5 superstring by means of the
Thermodynamic Bethe Ansatz requires an understanding of a companion 2d theory which …