Review of AdS/CFT Integrability,Chapter V.3: Scattering Amplitudes at Strong Coupling

Letters in Mathematical Physics - We review the computation of scattering amplitudes of planar maximally super-symmetric Yang–Mills at strong coupling. By using the AdS/CFT duality the...     

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.     

Central charges of Liouville and Toda theories from M5-branes

We show that the central charge of the Liouville and Toda theories of type A, D, and E can be reproduced by equivariantly integrating the anomaly eight-form of the corresponding six-dimensional N=(0,2) theories, which describe the low-energy dynamics of M5-branes.     

Affine <Emphasis Type="Italic">SL</Emphasis>(2) Conformal Blocks from 4d Gauge Theories

We study Nekrasov’s instanton partition function of four-dimensional N=2{\mathcal{N}=2} gauge theories in the presence of surface operators. This can be computed order by order in the instanton expansion by using results available in the mathematical literature. Focusing in the case of SU(2) quiver gauge theories, we find that the results agree with a modified version of the conformal blocks of affine SL(2) algebra. These conformal blocks provide, in the critical limit, the eigenfunctions of the corresponding quantized Hitchin Hamiltonians.     

Liouville Correlation Functions from Four-Dimensional Gauge Theories

We conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class of N=2{\mathcal{N}=2} SCFTs recently defined by one of the authors. We conduct extensive tests of the conjecture at genus 0, 1.