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Supersymmetric Yang-Mills theories can be characterized by a non-local and non-linear transformation of the bosonic fields (Nicolai map) mapping the interacting functional measure to that of a free theory, such that the Jacobi determinant…
We consider the matrix model approach to the anomalous dimension matrix in $\mathcal{N}=4$ super Yang--Mills theory. We construct the path integral representation for the anomalous dimension density matrix and analyze the resulting action.…
We provide details of the lattice construction of five-dimensional maximally supersymmetric Yang-Mills theory. The lattice theory is supersymmetric, gauge invariant and free from spectrum doublers. Such a supersymmetric lattice formulation…
Classical vacuum - pure gauge - solutions of Euclidean two-dimensional SU(2) Yang-Mills theories are studied. Topologically non-trivial vacua are found in a class of gauge group elements isomorphic to $S_2$. These solutions are unexpectedly…
We derive five-dimensional super Yang-Mills theory from mass-deformed ABJM theory by expanding about $S^2$ for large Chern-Simons level $K$. We obtain the Yang-Mills coupling constant $g_{YM}^2 = 4\pi^2 R/K$. If we consider $S^3/{\mb{Z}_K}$…
We present a complete classification, at the classical level, of the observables of topological Yang-Mills theories with an extended shift supersymmetry of N generators, in any space-time dimension. The observables are defined as the…
We consider the dimensional reduction of supersymmetric Yang-Mills on a Calabi-Yau 3-fold. We show by construction how the resulting cohomological theory is related to the balanced field theory of the Kaehler Yang-Mills equations introduced…
We generalize to topologically non-trivial gauge configurations the description of the Einstein-Yang-Mills system in terms of a noncommutative manifold, as was done previously by Chamseddine and Connes. Starting with an algebra bundle and a…
In this note, we evaluate the Weyl-invariant quadratic curvature tensors for the particular Weyl's gauge field constructed in the $3+1$-dimensional noncompact Weyl-Einstein-Yang-Mills model. We subsequently extend the model to its higher…
We formulate maximally supersymmetric Yang-Mills theory in five dimensions in light-cone superspace. The light-cone Hamiltonian is of the quadratic form and the theory can be understood as an oxidation of the N=4 Super Yang-Mills Theory in…
Gauge fields of semisimple groups of internal symmetries are massless and require the special techniques for guarantee their mass. Massive mechanisms usually contain transformations of shifts typical to nonsemisimple groups. We show that…
The planar Yang-Mills theory in three spatial dimensions is examined in a particular representation which explicitly embodies factorization. The effective planar Yang-Mills theory Hamiltonian is constructed in this representation.
We derive the spectra of D=2, SU(3) supersymmetric Yang-Mills quantum mechanics in all fermionic sectors. Moreover, we provide exact expressions for the corresponding eigenvectors in the sectors with none and one fermionic quantum. We also…
We present supersymmetric Yang-Mills theories in arbitrary even dimensions with the signature (9+m,1+m) where $m=0,1,2,...$ beyond ten-dimensions up to infinity. This formulation utilizes null-vectors and is a generalization of our previous…
We generalize the gradient flow equation for field theories with nonlinearly realized symmetry. Applying the formalism to super Yang-Mills theory, we construct a supersymmetric extension of the gradient flow equation. It can be shown that…
We construct super Yang-Mills theories with ${\cal N}=2, 4$ supersymmetries on the two-dimensional square lattice keeping one or two supercharges exactly. Along the same line as the previous paper \cite{sugino}, the construction is based on…
In order to have a new perspective on the long-standing problem of the mass gap in Yang-Mills theory, we study the quantum Yang-Mills theory in the presence of topologically nontrivial backgrounds in this paper. The topologically stable…
We discuss bosonic and supersymmetric Yang-Mills matrix models with compact semi-simple gauge group. We begin by finding convergence conditions for the partition and correlation functions. Moving on, we specialise to the SU(N) models with…
We present a twistor space that describes super null-lines on six-dimensional N=(1,1) superspace. We then show that there is a one-to-one correspondence between holomorphic vector bundles over this twistor space and solutions to the field…
We study supersymmetric and super Poincar\'e invariant deformations of ten-dimensional super Yang-Mills theory and of its dimensional reductions. We describe all infinitesimal super Poincar\'e invariant deformations of equations of motion…