Related papers: Yang-Mills Theory in Twistor Space
In the present paper we shall extend the gauge principle so that it will enlarge the original algebra of the Abelian gauge transformations found earlier in our studies of tensionless strings to the non-Abelian case. In this extension of the…
This Ph.D. thesis reaches two main results. The first one is represented by a detailed study, in Feynman gauge, of the perturbative ${\cal O}(g^4)$ contribution to a space-time Wilson loop, with respect to its (expected) Abelian-like time…
Using noncommutative geometry we do U(1) gauge theory on the permutation group $S_3$. Unlike usual lattice gauge theories the use of a nonAbelian group here as spacetime corresponds to a background Riemannian curvature. In this background…
We revisit the duality between five-dimensional supersymmetric gauge theories and deformations of two-dimensional Yang-Mills theory from a new perspective. We give a unified treatment of supersymmetric gauge theories in three and five…
Using methods of differential geometry, a discrete analog of the Yang-Mills equations in Minkowski space is constructed. The gauge transformation law in a discrete formulation is given and gauge invariance of discrete Yang-Mills equations…
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…
In this work we present a constructive proof that pure SU(3) Yang-Mills theory on R^4 exists as a nontrivial Wightman quantum field theory and exhibits a strictly positive mass gap. Our approach embeds the four-dimensional gauge theory as…
MHV diagrams give an efficient Feynman diagram-like formalism for calculating gauge theory scattering amplitudes on momentum space. Although they arise as the Feynman diagrams from an action on twistor space in an axial gauge, the main…
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…
The Yang-Mills functional integral is studied in an axial variant of 't Hooft's maximal Abelian gauge. In this gauge Gau\ss ' law can be completely resolved resulting in a description in terms of unconstrained variables. Compared to…
In this work, we set up the theoretical framework and indicate future applications of symmetric Yang--Mills fields to cosmology. We analyze the coset space dimensional reduction scheme to construct pure Yang--Mills fields on spacetimes…
The existence of interacting higher-spin theories is tightly constrained by many no-go theorems. In this paper, we construct a chiral, higher-spin generalization of Yang-Mills theory in flat space which avoids these no-go theorems and has…
This is the second part in a four-paper sequence, which establishes the Threshold Conjecture and the Soliton Bubbling vs.~Scattering Dichotomy for the hyperbolic Yang--Mills equation in the $(4+1)$-dimensional space-time. This paper…
In this paper we show that a particular twist of $\mathcal{N}=4$ super Yang-Mills in three dimensions with gauge group SU(2) possesses a set of classical vacua corresponding to the space of flat connections of the {\it complexified} gauge…
The non-linear nature of Yang-Mills theory presents a challenge for extracting exact classical solutions, which are useful for understanding non-perturbative vacuum structures. In this paper, an algebraic tensor ring decomposition framework…
A nonabelian class of massless/massive nonlinear gauge theories of Yang-Mills vector potentials coupled to Freedman-Townsend antisymmetric tensor potentials is constructed in four spacetime dimensions. These theories involve an extended…
This paper studies a class of four-dimensional quantum field theories which arise by quantizing local holomorphic field theories on twistor space. These theories have some remarkable properties: in particular, all correlation functions are…
We present the quantum Yang-Mills theory in the four-dimensional de Sitter ambient space formalism. In accordance with the SU$(3)$ gauge symmetry the interaction Lagrangian is formulated in terms of interacting color charged fields in…
It has been known for many years that, in Yang-Mills theories with $\mathcal{N}=4,2,2^*$ supersymmetry, certain nontrivial supersymmetric Wilson loops exist with v.e.v. either trivial or computable by localization that arises from a…
In this work, we introduce a novel approach to the problem of gauge choice for the Yang-Mills equation on the Minkowski space $\mathbb{R}^{1+3}$, which uses the Yang-Mills heat flow in a crucial way. As this approach does not possess the…