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We construct a two-dimensional N=8 supersymmetric quantum mechanics which inherits the most interesting properties of N=2, $d=4$ supersymmetric Yang-Mills theory. After dimensional reduction to one dimension in terms of field-strength, we…
We study four dimensional $SU(2)$ Yang-Mills theory with two massless adjoint Weyl fermions. When compactified on a spatial circle of size $L$ much smaller than the strong-coupling scale, this theory can be solved by weak-coupling…
The quasi-classical model in a gauge theory with the Yang-Mills (YM) field is developed. On a basis of the exact solution of the Dirac equation in the SU(N) gauge field, which is in the eikonal approximation, the Yang-Mills (YM) equations…
We present a lattice formulation for two-dimensional N=(2,2) and (4,4) supersymmetric Yang-Mills theories that resolves vacuum degeneracy for gauge fields without imposing admissibility conditions. Cases of U(N) and SU(N) gauge groups are…
I argue that a certain perturbative proximity exists between some supersymmetric and non-supersymmetric theories (namely, pure Yang-Mills and adjoint QCD with two flavors, adjQCD$_{N_f=2}$). I start with ${\mathcal N}=2$ super-Yang-Mills…
D=4, N=4 super-Yang-Mills theory has an off-shell superspace formulation in terms of pure spinor superfields, which is directly inherited from the D=10 theory. That superspace, in particular the choice of pure spinor variables, is less…
We present a series of four self-contained lectures on the following topics: (I) An introduction to 4-dimensional 1\leq N \leq 4 supersymmetric Yang-Mills theory, including particle and field contents, N=1 and N=2 superfield methods and the…
We show that (specifically scaled) equations of shear-free null geodesic congruences on the Minkowski space-time possess intrinsic self-dual, restricted gauge and algebraic structures. The complex eikonal, Weyl 2-spinor, $SL(2,\mathbb C)$…
The subject of this thesis are various ways to construct four-dimensional quantum field theories from string theory. In a first part we study the generation of a supersymmetric Yang-Mills theory, coupled to an adjoint chiral superfield,…
A particular dimensional reduction of SU(2N) Yang--Mills theory on $\Sigma \times S^2$, with $\Sigma$ a Riemann surface, yields an $S(U(N) \times U(N))$ gauge theory on $\Sigma$, with a matrix Higgs field. The SU(2N) self-dual Yang--Mills…
We show that $N=2$ and $N=4$ extended supersymmetric Yang-Mills theories in four space-time dimensions could be derived as action functionals for non-commutative spaces. The coupling of $N=1$ and $N=2$ super Yang-Mills to $N=1$ and $N=2$…
In this paper we construct super Yang-Mills theory in 10+2 dimensions, a number of dimensions that was not reached before in a unitary supersymmetric field theory, and show that this is the 2T-physics source of some cherished lower…
The relation between a nonlinear supersymmetic (NLSUSY) theory and a SUSY Yang-Mills (SYM) theory is studied for N = 3 SUSY in two-dimensional space-time. We explicitly show the NL/L SUSY relation for the (pure) SYM theory by means of…
Consistent interactions of spin 3/2 field that realize a nilpotent spinorial symmetry are presented. Based on our previous results on purely bosonic non-Abelian tensor with consistent interactions, we present a new system for interacting…
By considering N=2 string amplitudes we determine the (2+2)-dimensional target space action for the physical degrees of freedom: self-dual gravity and self-dual Yang-Mills, together with their respective infinite towers of higher-spin…
Starting from a self-dual $SU(\infty)$ Yang-Mills theory in $(2+2)$ dimensions, the Plebanski second heavenly equation is obtained after a suitable dimensional reduction. The self-dual gravitational background is the cotangent space of the…
Within the superfield approach, we consider the duality between the supersymmetric Maxwell-Chern-Simons and self-dual theories in three spacetime dimensions. Using a gauge embedding method, we construct the dual theory to the self-dual…
We construct SU($N$) super Yang-Mills theories with extended supersymmetry on hypercubic lattices of various dimensions keeping one or two supercharges exactly. It is based on topological field theory formulation for the super Yang-Mills…
Global supersymmetries of the S-matrices of N = 2, 4, 8 supersymmetric Yang-Mills theories in three spacetime dimensions (without matter hypermultiplets) are shown to be SU(1|1), SU(2|2) and SU(2|2) X SU(2|2) respectively. These symmetries…
We review recent work on the study of N=2 super Yang-Mills theory with gauge group SU(N) from the point of view of the Whitham hierarchy, mainly focusing on three main results: (i) We develop a new recursive method to compute the whole…