Alessandro Torrielli

Review of AdS/CFT Integrability: An Overview

This is the introductory chapter of a review collection on integrability in the context of the AdS/CFT correspondence. In the collection, we present an overview of the achievements and the status of this subject as of the year 2010.

Hopf algebra structure of the AdS/CFT S-matrix

We formulate the Hopf algebra underlying the su(2/2) world sheet S-matrix of the AdS{sub 5}xS{sup 5} string in the AdS/CFT correspondence. For this we extend the previous construction in the su(1/2) subsector due to Janik to the full algebra by specifying the action of the coproduct and the antipode on the remaining generators. The nontriviality of the coproduct is determined by length-changing effects and results in an unusual central braiding. As an application we explicitly determine the antiparticle representation by means of the established antipode.

Wrapping interactions and the genus expansion of the 2-point function of composite operators

We perform a systematic analysis of wrapping interactions for a general class of theories with color degrees of freedom, including N=4 SYM. Wrapping interactions arise in the genus expansion of the 2-point function of composite operators as finite size effects that start to appear at a certain order in the coupling constant at which the range of the interaction is equal to the length of the operators. We analyze in detail the relevant genus expansions, and introduce a strategy to single out the wrapping contributions, based on adding spectator fields. We use a toy model to demonstrate our procedure, performing all computations explicitly. Although completely general, our treatment should be particularly useful for applications to the recent problem of wrapping contributions in some checks of the AdS/CFT correspondence.

On the massless modes of the AdS3/CFT2 integrable systems

A bstractWe make a proposal for incorporating massless modes into the spin-chain of the AdS3/CF T2 integrable system. We do this by considering the α → 0 limit of the alternating

A secret symmetry of the AdS/CFT S-matrix

\mathfrak{d}{{\left( {2,1;\alpha } \right)}^2}

The all-loop integrable spin-chain for strings on AdS3 × S 3 × T 4: the massive sector

spin-chain constructed in arXiv:1106.2558. In the process we encounter integrable spin-chains with non-irreducible representations at some of thei r sites. We investigate their properties and construct their R-matrices in terms of Yangians.

Dressing phases of AdS3/CFT2

We find a new quantum Yangian symmetry of the AdS/CFT S-matrix, which complements the original (2|2) symmetry to (2|2) and does not have a Lie algebra analog. Our finding is motivated by the Yangian double structure discovered at the classical level.

5D partition functions, q-Virasoro systems and integrable spin-chains

A bstractWe bootstrap the all-loop dynamic S-matrix for the homogeneous

Classical r-matrix of the su(2|2) SYM spin-chain

\mathfrak{p}\mathfrak{s}\mathfrak{u}

The bound state S-matrix for AdS5×S5 superstring

(1, 1|2)2 spin-chain believed to correspond to the discretization of the massive modes of string theory on AdS3 × S3 × T4. The S-matrix is the tensor product of two copies of the