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We discuss the algebraic renormalization of the Yang--Mills gauge field theory in the presence of translations. Due to the translations the algebra between Sorella's $\d$--operator, the exterior derivative and the BRST--operator closes.…
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…
The Yang-Mills equations are formulated in the form of generalized Maurer-Cartan equations, such that the corresponding algebraic operations are shown to satisfy the defining relations of homotopy Lie superalgebra.
A residue formula which evaluates any correlation function of topological $SU_n$ Yang-Mills theory with arbitrary magnetic flux insertion in two dimensions are obtained. Deformations of the system by two form operators are investigated in…
Some aspects of the multidimensional soliton geometry are considered. It is shown that some simples (2+1)-dimensional equations are exact reductions of the Self-Dual Yang-Mills equation or its higher hierarchy.
In this paper, we consider the deformed Hermitian-Yang-Mills equation on closed almost Hermitian manifolds. In the case of hypercritical phase, we derive a priori estimates under the existence of an admissible $\mathcal{C}$-subsolution. As…
We use a very simple version of the optimized (linear) $\delta $ - expansion by scaling the free part of the Lagrangian with a variational parameter. This method is well suited to calculate the renormalized coupling constant in terms of the…
This paper proposes an algorithm for computing regularized solutions to linear rational expectations models. The algorithm allows for regularization cross-sectionally as well as across frequencies. A variety of numerical examples illustrate…
The computation of higher derivative corrections to the low energy effective actions of ${\cal N}=2$ gauge theories is considered. In particular, higher derivative corrections are computed for four dimensional ${\cal N}=2$ super Yang-Mills…
In the present paper it is shown that the Yang-Mills equation can be represented as the equation of the non-linear electromagnetic waves superposition. The research of the topological characteristics of this representation allows us to…
A surface of codimension higher than one embedded in an ambient space possesses a connection associated with the rotational freedom of its normal vector fields. We examine the Yang-Mills functional associated with this connection. The…
A gauge invariant infrared regularization of the Yang-Mills theory applicable beyond perturbation theory is constructed.
We present an action for noncommutative supersymmetric Yang-Mills theory in ten-dimensions, and confirm its invariance under supersymmetry. We next add higher-order derivative terms to such a noncommutative supersymmetric action. These…
Recent results obtained within the Hamiltonian approach to continuum Yang-Mills theory in Coulomb gauge are reviewed.
By exploiting standard facts about $N=1$ and $N=2$ supersymmetric Yang-Mills theory, the Donaldson invariants of four-manifolds that admit a Kahler metric can be computed. The results are in agreement with available mathematical…
In this paper we provide a geometric derivation of the master loop equation for the lattice Yang-Mills model with structure group $G \in \{SO(N),SU(N), U(N)\}$. This approach is based on integration by parts on $G$. In the appendix we…
A recently proposed integral representation for permanents is rederived using only elementary combinatorics. For this proof the assumption that the matrix, for which the permanent is calculated, has an inverse is not necessary.
The Yang--Mills gradient flow and its extension to the fermion field provide a very general method to obtain renormalized observables in gauge theory. The method is applicable also with non-perturbative regularization such as lattice. The…
This partially expository paper provides a view of Yang-Mills equations from the perspective of complex variables, operator theory, and $C^{*}$-algebras. Through operator-valued pluriharmonic and skew-Hermitian differential forms, it…
In this short note, we propose an unified method to derive formulas for derivations conjugated by exponential functions on an almost complex manifold. In v3, we corrected some mistakes in previous versions.