Related papers: Baxter equation for long-range SL(2|1) magnet

We construct a closed system of equations describing the quark--anti-quark potential at any coupling in planar N=4 supersymmetric Yang-Mills theory. It is based on the Quantum Spectral Curve method supplemented with a novel type of…

We consider the modified (or twisted) Yang-Baxter equations for the $SL_{q}(N)$ groups and $SL_{q}(N|M)$ supergroups. The general solutions for these equations are presented in the case of the linear quantum (super)groups. The introduction…

We compute the nonplanar contribution to the universal anomalous dimension of the SU(4)-singlet twist-two operators in N=4 supersymmetric Yang-Mills theory at four loops through Lorentz spin 18. From this, we numerically evaluate the…

We discuss composite operators in N=4 super Yang-Mills theory and their realisations as superfields on different superspaces. The superfields that realise various operators on analytic superspace may be different in the free, interacting…

The dilatation generator measures the scaling dimensions of local operators in a conformal field theory. In this thesis we consider the example of maximally supersymmetric gauge theory in four dimensions and develop and extend techniques to…

We study scalar excitations of high spin operators in N=4 super Yang-Mills theory, which are dual to solitons propagating on a long folded string in AdS_3 x S^1. In the spin chain description of the gauge theory, these are associated to…

Recently it was established that the one-loop planar dilatation generator of N=4 Super Yang-Mills theory may be identified, in some restricted cases, with the Hamiltonians of various integrable quantum spin chains. In particular Minahan and…

Operators dual to strings attached to giant graviton branes in AdS$_5\times$S$^5$ can be described rather explicitly in the dual ${\cal N} = 4$ super Yang-Mills theory. They have a bare dimension of order $N$ so that for these operators the…

We discuss the properties of quarter-BPS local operators in four dimensional ${\cal N}=1$ supersymmetric Yang-Mills theory using the formalism of holomorphic twists. We study loop corrections both to the space of local operators and to…

We propose a method to calculate the expectation values of an operator similar to the Wilson loop in the large N limit of field theories. We consider N=4 3+1 dimensional super-Yang-Mills. The prescription involves calculating the area of a…

We analyse the renormalisation properties of composite operators of scalar fields in the N=2 Super Yang-Mills theory. We compute the matrix of anomalous dimensions in the planar limit at one-loop order in the 't Hooft coupling, and show…

We analyze the slow roll limit of the massive version of time-dependent Yang--Mills type matrix model. We find that this limit reproduces the one-loop non-Hermitian matrix model, describing the dilatations of the local gauge invariant…

We derive and investigate the S-matrix for the su(2|3) dynamic spin chain and for planar N=4 super Yang-Mills. Due to the large amount of residual symmetry in the excitation picture, the S-matrix turns out to be fully constrained up to an…

We explicitly construct a configuration of ${\cal N}=4$ supersymmetry Yang-Mills theory with gauge group $U(N)$ on an interval on length $L$ with a D5-like boundary condition on one end and an NS5-like boundary condition on the other. For…

In this paper we propose a simple method for building exactly solvable multi-parameter spectral equations which in turn can be used for constructing completely integrable and exactly solvable quantum systems. The method is based on the use…

Correlators of Wilson loop operators with O_4=Tr(F_{\mu\nu}^2+...) are computed in N=4 super-Yang-Mills theory using the AdS/CFT correspondence. The results are compared with the leading order perturbative computations. As a consequence of…

At the previous congress (CRM 6), we reviewed the construction of Yang-Baxter operators from associative algebras, and presented some (colored) bialgebras and Yang-Baxter systems related to them. The current talk deals with Yang-Baxter…

We show that the BMN operators arise from the expansion of the Wilson loop in four-dimensional N=4 super Yang-Mills theory. The Wilson loop we consider is obtained from ``dimensional reduction'' of ten-dimensional N=1 super Yang-Mills…

The supersymmetry transformation relating the Konishi operator to its lowest descendant in the 10 of SU(4) is not manifest in the N=1 formulation of the theory but rather uses an equation of motion. On the classical level one finds one…

We investigate various perturbative properties of the deformed N=4 SYM theory. We carry out a three-loops calculation of the chiral matter superfield propagator and derive the condition on the couplings for maintaining finiteness at this…