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 the recent progress towards applying worldsheet integrability techniques to the
${\rm Ad}{{{\rm S}} _ {3}}/{\rm CF}{{{\rm T}} _ {2}} $ correspondence to find its all-loop S matrix …

We review the recent advances towards finding the spectrum of the AdS 5× S 5 superstring.
We thoroughly explain the theoretical techniques which should be useful for the ultimate …

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 …

Moving from the mirror theory Bethe–Yang equations proposed by Arutyunov and Frolov, we
derive the thermodynamic Bethe ansatz equations which should control the spectrum of the …

A bstract We propose a nonperturbative framework to study general correlation functions of
single-trace operators in\(\mathcal {N}\)= 4 supersymmetric Yang-Mills theory at large N. The …

We use the string hypothesis for the mirror theory to derive the Thermodynamic Bethe
Ansatz equations for the AdS 5× S 5 mirror model. We further demonstrate how these …

We consider the world-sheet S matrix of superstrings on an AdS 3× S 3× T 4 NS-NS
background in uniform light-cone gauge. We argue that scattering is given by a CDD factor …

The first part of these lecture notes is mostly devoted to a comparative discussion of the
three basic large $ N $ limits, which apply to fields which are vectors, matrices, or tensors of …

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 …