Related papers: Symplectic Yang-Mills theory, Ricci tensor, and co…
We define supersymmetric Yang-Mills theory on an arbitrary two-dimensional lattice (polygon decomposition) with preserving one supercharge. When a smooth Riemann surface $\Sigma_g$ with genus $g$ emerges as an appropriate continuum limit of…
In the present paper we analyze algebraic structures arising in Yang-Mills theory. The paper should be considered as a part of a project started with a paper "On maximally supersymmetric Yang-Mills theories" devoted to maximally…
A few years ago H. Morales and the author introduced a type of generalized derivative that contained both vector and scalar boson fields. Here it is shown how to construct a full-fledged generalized Yang-Mills theory through the…
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 quantize pure 2d Yang-Mills theory on an arbitrary Riemann surface in the gauge where the field strength is diagonal. Twisted sectors originate, as in Matrix string theory, from permutations of the eigenvalues around homotopically…
Numerical simulations of supersymmetric theories on the lattice are intricate and challenging with respect to their theoretical foundations and algorithmic realisation. Nevertheless, the simulations of a four-dimensional supersymmetric…
We discuss some of the recent developments of N=1 super Yang-Mills theories in the context of the gauge-string correspondence.
The low energy effective Lagrangian for $N\es 2$ supersymmetric Yang-Mills theory, proposed by Seiberg and Witten is shown to be the unique solution, assuming only that supersymmetry is unbroken and that the number of strong-coupling…
We present some of the latest results from our numerical investigations of N=4 supersymmetric Yang--Mills theory formulated on a space-time lattice. Based on a construction that exactly preserves a single supersymmetry at non-zero lattice…
We proved a uniqueness theorem of tangent connections for a Yang-Mills connection with an isolated singularity with a quadratic growth of the curvature at the singularity. We also obtained controls over the rate of the asymptotic…
Gauge symmetries remove unphysical states and guarantee that field theories are free from the pathologies associated with these states. In this work we find a set of general conditions that guarantee the removal of unphysical states in…
The Yang-Mills theory lies at the heart of our understanding of elementary particle interactions. For the strong nuclear forces, we must understand this theory in the strong coupling regime. The primary technique for this is the lattice.…
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…
For the spinning superparticle we construct the pull-back of the world-line path integral to super moduli space in the Hamiltonian formulation. We describe the underlying geometric decomposition of super moduli space. Algebraically, this…
We summarize some of the main ideas and results around symplectic field theory, from its early inception up to recent and ongoing developments.
In this brief review, I summarize the current theoretical knowledge in supersymmetry on the lattice, with special emphasis on recent results in the framework of N=1 supersymmetric Yang Mills theory, Wess-Zumino model and Yang-Mills theory…
We develop the complete composite theory of gravity, in which the gauge vector fields of the Yang-Mills theory with Lorentz symmetry group are expressed in terms of the tetrad variables obtained from the decomposition of a metric. A key…
We derive closed formulae for the first examples of non-algebraic, elliptic `leading singularities' in planar, maximally supersymmetric Yang-Mills theory and show that they are Yangian-invariant.
Yang-Baxter R operators symmetric with respect to the orthogonal and symplectic algebras are considered in an uniform way. Explicit forms for the spinorial and metaplectic R operators are obtained. L operators, obeying the RLL relation with…
A geometrization of the Yang-Mills field, by which an SU(2) gauge theory becomes equivalent to a 3-space geometry - or optical system - is examined. In a first step, ambient space remains Euclidean and current problems on flat space can be…