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These lectures provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories. After a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories, I analyze the qualitative…
This article gives an overview of many of the recent developments in understanding the structure of relativistic scattering amplitudes in gauge theories ranging from QCD to N=4 super-Yang-Mills theory, as well as (super)gravity. I also…
We compute the boundary scattering amplitudes of the breathers of the supersymmetric sine-Gordon model using the fusion of the soliton-antisoliton pair scattering with the boundary with a known result of the soliton boundary scattering…
We examine the dual correspondence between holographic IIB superstring theory and N=4 super Yang-Mills theory at finite values of the coupling constants. In particular we analyze a field theory strong-coupling expansion which is the S-dual…
Motivated by the computation of scattering amplitudes at strong coupling, we consider minimal area surfaces in AdS_5 which end on a null polygonal contour at the boundary. We map the classical problem of finding the surface into an SU(4)…
We discuss the dependence of pure Yang-Mills equation of state on the choice of gauge algebra. In the confined phase, we generalize to an arbitrary simple gauge algebra Meyer's proposal of modelling the Yang-Mills matter by an ideal…
We consider gluon and gluino scattering amplitudes in large N beta-deformed N=4 SYM with real beta. A direct inspection of the planar diagrams shows that the scattering amplitudes to all orders in perturbation theory are the same as in the…
We extend the analysis of Alday and Maldacena for obtaining gluon scattering amplitudes at strong coupling to include external massive quark states. Our quarks are actually the N=2 hypermultiplets which arise when D7-brane probes are…
Tree-level scattering amplitudes in N=4 super Yang-Mills theory have recently been shown to transform covariantly with respect to a 'dual' superconformal symmetry algebra, thus extending the conventional superconformal symmetry algebra…
We study tree-level celestial amplitudes in Yang-Mills theory -- Mellin transforms of multi-gluon scattering amplitudes that convert them into the correlators of conformal primary fields on two-dimensional celestial sphere. By using purely…
This paper deals with various interrelations between strings and surfaces in three dimensional ambient space, two dimensional integrable models and two dimensional and four dimensional decomposed SU(2) Yang-Mills theories. Initially, a…
The S-matrix of a theory often exhibits symmetries which are not manifest from the viewpoint of its Lagrangian. For instance, powerful constraints on scattering amplitudes are imposed by the dual conformal symmetry of planar 4d…
We investigate the space of massive two-dimensional theories with a global U(N) symmetry and no bound states. Following S-matrix bootstrap principles, we establish rigorous bounds on the space of consistent $2 \rightarrow 2$ scattering…
By superposition of regular gauge instantons or merons, ensembles of gauge fields are constructed which describe the confining phase of SU(2) Yang-Mills theory. Various properties of the Wilson loops, the gluon condensate and the…
Using the boundary Yang-Baxter equations and exact results on the bulk $S$-matrices, we compute exact boundary scattering amplitudes of the supersymmetric sine-Gordon model with integrable boundary potentials.
Following Alday and Maldacena, we describe a string theory method to compute the strong coupling behavior of the scattering amplitudes of quarks and gluons in planar N=2 super Yang-Mills theory in the probe approximation. Explicit…
We study the maximally-helicity-violating (MHV) six-gluon scattering amplitude in planar $\mathcal{N} = 4$ super-Yang-Mills theory at finite coupling when all three cross ratios are small. It exhibits a double logarithmic scaling in the…
We conjecture a new set of analytic relations for scattering amplitudes in planar N=4 super Yang-Mills theory. They generalise the Steinmann relations and are expressed in terms of the cluster algebras associated to Gr(4,n). In terms of the…
These notes were given as lectures at the CERN Winter School on Supergravity, Strings and Gauge Theory 2010. We describe the structure of scattering amplitudes in gauge theories, focussing on the maximally supersymmetric theory to highlight…
Using cutting techniques we obtain the two-loop N=4 super-Yang-Mills helicity amplitudes for four-gluon scattering in terms of scalar integral functions. The N=4 amplitudes are considerably simpler than corresponding QCD amplitudes and…