Related papers: Four-loop perturbative Konishi from strings and fi…

We present a proof of perturbative unitarity for $\mathcal{N}=4$ SYM, following from the geometry of the amplituhedron. This proof is valid for amplitudes of arbitrary multiplicity $n$, loop order $L$ and MHV degree $k$.

We give the correct analytic expression of a finite integral appearing in the four-loop computation of the renormalization-group functions for the two-dimensional nonlinear sigma-model on the square lattice with standard action, explaining…

The three dimensional N=2 supersymmetric Chern-Simons theory coupled to matter fields, possibly deformed by a superpotential, give rise to a large class of exactly conformal theories with Lagrangian descriptions. These theories can be…

We discuss the action of SL(2,Z) on local operators in D=4, N=4 SYM theory in the superconformal phase. The modular property of the operator's scaling dimension determines whether the operator transforms as a singlet, or covariantly, as…

We study the commutative limit of the non-commutative maximally supersymmetric Yang-Mills theory in four dimensions (N=4 SYM). The commutative limits of non-commutative spaces are important in particular in the applications of…

The the duality between ${\cal N}=4$ SYM and the AdS$_5\times\;$S$^5$ superstring appears to enjoy quantum integrability in the planar limit, which allowed to devise powerful methods ostensibly solving the spectral problem. However,…

We study tree level scattering amplitudes of four massless states in the double scaled little string theory, and compare them to perturbative loop amplitudes in six-dimensional super-Yang-Mills theory. The little string amplitudes are…

We revisit the calculation of instanton effects in correlation functions in ${\cal N}=4$ SYM involving the Konishi operator and operators of twist two. Previous studies revealed that the scaling dimensions and the OPE coefficients of these…

We investigate finite-size corrections to anomalous dimensions of large-spin twist-two operators in the planar maximally supersymmetric Yang-Mills theory. We develop a framework for analysis of these corrections, that is complementary to…

We consider a class of N=2 conformal SU(N) SYM theories in four dimensions with matter in the fundamental, two-index symmetric and anti-symmetric representations, and study the corresponding matrix model provided by localization on a sphere…

In perturbation theory, the anomalous dimensions of twist-two operators have poles at negative or small positive integer values of spin and therefore must be resummed at these points. It was observed earlier that a certain quadratic…

It has been recently proposed that string theory in the background of a plane wave corresponds to a certain subsector of the N=4 supersymmetric Yang-Mills theory. This correspondence follows as a limit of the AdS/CFT duality. As a…

In this talk we present the result for the $n_f$ dependent piece of the three-loop cusp anomalous dimension in QCD. Remarkably, it is parametrized by the same simple functions appearing in analogous anomalous dimensions in ${\mathcal N}=4$…

Beginning with the planar limit of N=4 SYM theory, we study planar diagrams for field theory deformations of N=4 which are marginal at the free field theory level. We show that the requirement of integrability of the full one loop…

We compute quantum corrections to finite-size effects for various dyonic giant magnons in the AdS_4 x CP^3 in two different approaches. The off-shell algebraic curve method is used to quantize the classical string configurations in…

In the context of the superconformal N=4 SYM theory the Konishi anomaly can be viewed as the descendant $K_{10}$ of the Konishi multiplet in the 10 of SU(4), carrying the anomalous dimension of the multiplet. Another descendant $O_{10}$…

We examine in detail the structure of the Regge limit of the (nonplanar) ${\cal N}=4$ SYM four-point amplitude. We begin by developing a basis of color factors $C_{ik}$ suitable for the Regge limit of the amplitude at any loop order, and…

We investigate N=4 noncommutative super Yang-Mills (SYM) theory. We compute the one-loop four gauge boson scattering amplitude on parallel Dp-branes, and find the corresponding contribution to the noncommutative SYM one-loop action in a…

We derive the one loop mixing matrix for anomalous dimensions in N=4 Super Yang-Mills. We show that this matrix can be identified with the Hamiltonian of an integrable SO(6) spin chain with vector sites. We then use the Bethe ansatz to find…

We derive a finite set of nonlinear integral equations for describing the finite size dependence of the ground state energy of the O(4) nonlinear sigma model. By modifying the kernel functions of these equations we propose nonlinear…