Related papers: Systematic Extraction of Exact Yang-Mills Solution…
We construct a manifestly gauge invariant Exact Renormalisation Group (ERG) whose form is suitable for computation in SU(N) Yang-Mills theory, beyond one-loop. An effective cutoff is implemented by embedding the physical SU(N) theory in a…
These notes comprise the first of two articles devoted to the construction of exact solutions of noncommutative gauge theory in two spacetime dimensions. This first part deals solely with the classical theory on a noncommutative torus.…
We consider pure SU(2) Yang-Mills theory on four-dimensional de Sitter space dS$_4$ and construct a smooth and spatially homogeneous magnetic solution to the Yang-Mills equations. Slicing dS$_4$ as ${\mathbb R}\times S^3$, via an…
We solve exactly the Dyson-Schwinger equations for Yang-Mills theory in 3 and 4 dimensions. This permits us to obtain the exact correlation functions till order 2. In this way, the spectrum of the theory is straightforwardly obtained and…
Using a Dyson--Schwinger approach, we perform an analysis of the non-trivial ground state of thermal $SU(N)$ Yang--Mills theory in the non-perturbative regime where chiral symmetry is dynamically broken by a mass gap. Basic thermodynamic…
Dyson-Schwinger equations (DSEs) are a non-perturbative way to express n-point functions in quantum field theory. Working in Euclidean space and in Landau gauge, for example, one can study the quark propagator Dyson-Schwinger equation in…
The main objective of this thesis is to present a new analytical framework for low-energy QCD that goes under the name of massive, or "screened", perturbative expansion. The massive perturbative expansion is motivated by the phenomenon of…
An example of higher-derivative theory with a non-Abelian gauge symmetry is proposed. In the free limit, the model describes the multiplet of vector fields, being subjected to the extended Chern-Simons equations. The theory admits a single…
By making use of the background field method, we derive a novel reformulation of the Yang-Mills theory which was proposed recently by the author to derive quark confinement in QCD. This reformulation identifies the Yang-Mills theory with a…
I provide a new idea based on geometric analysis to obtain a positive mass gap in pure non-abelian renormalizable Yang-Mills theory. The orbit space, that is the space of connections of Yang-Mills theory modulo gauge transformations, is…
N=2 supersymmetric Yang--Mills theories coupled to matter are considered in the Wess--Zumino gauge. The supersymmetries are realized nonlinearly and the anticommutator between two susy charges gives, in addition to translations, gauge…
Scattering amplitudes in Yang-Mills-Einstein theories have been investigated mostly for compact gauge groups. While non-compact gauge groups are not physically viable in Yang-Mills theory, non-compact gaugings feature prominently in the…
A Yang-Mills type gauge theory of gravity is shown to have a structure richer than that of Einstein's General Theory of Relativity. By elevating the full connections to independent dynamical gauge fields, the theory admits non-trivial…
The method of reduction of a non-Abelian gauge theory to the corresponding unconstrained system is exemplified for SU(2) Yang-Mills field theory. The reduced Hamiltonian which describes the dynamics of the gauge invariant variables is…
Yang-Mills theory has extended well beyond its original role in describing the strong force and now emerges as an effective theory in condensed matter, ultracold atomic, and photonic systems. In these systems, the theory has been successful…
We present a reformulation of SU(2) Yang-Mills theory in the maximal Abelian gauge, where the non-Abelian gauge field components are exactly integrated out at the expense of a new Abelian tensor field. The latter can be treated in a…
The partition function of $\mathcal{N}=2$ super Yang-Mills theories with arbitrary simple gauge group coupled to a self-dual $\Omega$-background is shown to be fully determined by studying the renormalization group equations relevant to the…
We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are…
We investigate mass deformation of twisted superalgebra of U(N) super Yang-Mills (SYM) theories in several models and in several dimensions, motivated by the method formulated in [1]. We show that there are several ways to perform the…
Yang-Mills theories are an important building block of the standard model and in particular of quantum chromodynamics. Its correlation functions describe the behavior of its elementary particles, the gauge bosons. In quantum chromodynamics,…