Luis F. Alday

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

Gluon scattering amplitudes at strong coupling

{\mathcal{N}=2}

Comments on operators with large spin

SCFTs recently defined by one of the authors. We conduct extensive tests of the conjecture at genus 0, 1.

Y-system for scattering amplitudes

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.

Thermodynamic bubble ansatz

We describe how to compute planar gluon scattering amplitudes at strong coupling in = 4 super Yang Mills by using the gauge/string duality. The computation boils down to finding a certain classical string configuration whose boundary conditions are determined by the gluon momenta. The results are infrared divergent. We introduce the gravity version of dimensional regularization to define finite quantities. The leading and subleading IR divergencies are characterized by two functions of the coupling that we compute at strong coupling. We compute also the full finite form for the four point amplitude and we find agreement with a recent ansatz by Bern, Dixon and Smirnov.

An operator product expansion for polygonal null Wilson loops

Recently, a duality between Liouville theory and four dimensional

Null polygonal Wilson loops and minimal surfaces in Anti-de-Sitter space

\mathcal{N} = 2

From correlation functions to Wilson loops

gauge theory has been uncovered by some of the authors. We consider the role of extended objects in gauge theory, surface operators and line operators, under this correspondence. We map such objects to specific operators in Liouville theory. We employ this connection to compute the expectation value of general supersymmetric ’t Hooft-Wilson line operators in a variety of