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Based on an idea due to Bardeen and Pearson, we formulate the light-front Hamiltonian problem for SU(N) Yang-Mills theory in 2+1 dimensions using two continuous space-time dimensions with the remaining space dimension discretized on a…
We present a study of the effective string that describes the infrared dynamics of SU(2) Yang-Mills theory in three dimensions. By combining high-precision lattice simulation results for Polyakov-loop correlators at finite temperatures…
We construct a lattice formulation of a mass-deformed two-dimensional N=(8,8) super Yang-Mills theory with preserving two supercharges exactly. Gauge fields are represented by compact unitary link variables, and the exact supercharges on…
This report presents some studies of the gauge/string theory correspondence, a deep relation that is possible to establish between quantum field theories with local gauge symmetry and superstring theories including gravity. In its original…
We describe a class of six-dimensional conformal field theories that have some properties in common with and possibly are related to a subsector of the tensionless string theories. The latter theories can for example give rise to…
A complexification of the twisted $\N=2$ theory allows one to determine the N=4 Yang--Mills theory in its third twist formulation. The imaginary part of the gauge symmetry is used to eliminate two scalars fields and create gauge covariant…
The fluxtrap background of string theory provides a transparent and algorithmic way of constructing supersymmetric gauge theories with both mass and Omega-type deformations in various dimensions. In this article, we review a number of…
In this note we establish the explicit relation between correlation functions in ${\cal N} = 4$ SUSY Yang--Mills theory on $S^3\times R$ in a double scaling limit and scattering amplitudes of the String Theory on the pp-wave background. The…
Five-dimensional $\mathcal{N}=1$ supersymmetric Yang-Mills theories are investigated from the viewpoint of random plane partitions. It is shown that random plane partitions are factorizable as q-deformed random partitions so that they admit…
We propose a 5-dimensional definition for the physical 4D-Yang-Mills theory. The fifth dimension corresponds to the Monte-Carlo time of numerical simulations of QCD_4. The 5-dimensional theory is a well-defined topological quantum field…
The N=2 supersymmetric Yang-Mills theory is formulated on the lattice. The feasibility of numerical simulations is discussed.
We review here some of the checks of string-string duality between N=2, D=4 Heterotic and Type II models. The heterotic low energy field theory is reproduced on the type II side. It is also shown to be a generalization in the string context…
A previous study of the Kawai, Lewellen and Tye (KLT) relations between gravity and gauge theories, imposed by the relationship of closed and open strings, are here extended in the light of general relativity and Yang-Mills theory as…
When eight-dimensional instantons, satisfying F \wedge F = \pm \star_8 (F\wedge F), shrink to zero size, we find stringy objects in higher order ten-dimensional Yang-Mills (viewed as a low-energy limit of open string theory). The associated…
We calculate the k=2 string tensions in SU(4) and SU(5) gauge theories in 3+1 dimensions, and compare them to the k=1 fundamental string tensions. We find, from the continuum extrapolation of our lattice calculations, that K(k=2)/K(k=1) =…
In the first part of these lectures we will review the main aspects of large N QCD and the explicit results obtained from it. Then, after a review of the properties of N=4 super Yang-Mills, type IIB string theory and of AdS space, we…
Recent progress in understanding (2+1)-dimensional Yang-Mills (YM_{2+1}) theory via the use of gauge-invariant variables is reviewed. Among other things, we discuss the vacuum wavefunction, an analytic calculation of the string tension and…
A brief review of the status of duality symmetries in string theory is presented. The evidence is accumulating rapidly that an enormous group of duality symmetries, including perturbative T dualities and non-perturbative S-dualities,…
In recent years a new class of supersymmetric lattice theories have been proposed which retain one or more exact supersymmetries for non-zero lattice spacing. Recently there has been some controversy in the literature concerning whether…
The ${\cal N} = 2^*$ Yang-Mills theory in four dimensions is a non-conformal theory that appears as a mass deformation of maximally supersymmetric ${\cal N} = 4$ Yang-Mills theory. This theory also takes part in the AdS/CFT correspondence…