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 …

A bstract It is a long-standing conjecture that any CFT with a large central charge and a large
gap∆ gap in the spectrum of higher-spin single-trace operators must be dual to a local …

Supersymmetry plays prominent roles in the study of quantum field theory and in many
proposals for potential new physics beyond the standard model. Lattice field theory provides …

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 …

A bstract We compute 1/λ corrections to the four-point functions of half-BPS operators in SU
(N)\(\mathcal {N}\)= 4 super-Yang-Mills theory at large N and large't Hooft coupling λ=\({g} …

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 …

A bstract We explicitly rewrite the path integral for the free or critical O (N)(or U (N)) bosonic
vector models in d space-time dimensions as a path integral over fields (including massless …

We implement the conformal bootstrap for N= 4 superconformal field theories in four
dimensions. The consistency of the four-point function of the stress-energy tensor multiplet …

We introduce the AdS/CFT correspondence as a natural extension of QFT in a fixed AdS
background. We start by reviewing some general concepts of CFT, including the embedding …

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 …