Related papers: Renormalization Proof for Spontaneously broken Yan…
We reconsider the renormalizability of topological Yang-Mills field theories in (anti-)self-dual Landau gauges. By employing algebraic renormalization techniques we show that there is only one independent renormalization. Moreover, due to…
In paper I of this series on fluid turbulence we showed that exact resummations of the perturbative theory of the structure functions of velocity differences result in a finite (order by order) theory. These findings exclude any known…
The Yang-Mills gradient flow for QCD-like theories is generalized by including a fermionic matter term in the gauge field flow equation. We combine this with two different flow equations for the fermionic degrees of freedom. The solutions…
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…
The renormalization of N=1 Super Yang-Mills theory is analysed in the Wess-Zumino gauge, employing the Landau condition. An all orders proof of the renormalizability of the theory is given by means of the Algebraic Renormalization…
The study of renormalization of Yang-Mills fields in the light-front gauge has always been a delicate subject in that divergent {\em non-local} terms arise from the calculations of Feynman diagrams. In this short paper we show that this…
In this short Note, we establish that the constant $C_1$ in Lemma $0.4$ of the correction (Correction to Section 19.2 of Ricci Flow and the Poincare Conjecture, arXiv/math/DG:1512.00699 (2015)) by John Morgan and Gang Tian to their Clay…
This paper proves a general Uhlenbeck compactness theorem for sequences of solutions of Yang-Mills flow on Riemannian manifolds of dimension $n \geq 4,$ including rectifiability of the singular set at finite or infinite time.
A formulation of $\mathcal{N} = 2$ supersymmetric Yang-Mills theory with a spacetime-dependent gauge coupling allows to study the breaking of conformal symmetry at the quantum level. The theory has an energy-momentum tensor that is only…
In earlier work we proposed a string theory dual to two dimensional Yang-Mills theory at zero coupling (which can also be thought of as a $BF$ theory), given by a Polyakov-like generalization of Ho\v rava's topological rigid string theory,…
We consider the Yangs-Mills equations in 4+1 dimensions. This is the energy critical case and we show that it admits a family of solutions which blow up in finite time. They are obtained by the spherically symmetric ansatz in the SO(4)…
We study the behaviour of the flux tube in the reconfined phase of the trace deformed $\mathrm{SU}(2)$ Yang-Mills theory in (2 + 1) dimensions. In this phase the Polyakov loop has a vanishing expectation value (and center symmetry is…
I give an overview over some work on rigorous renormalization theory based on the differential flow equations of the Wilson-Wegner renormalization group. I first consider massive Euclidean $\phi_4^4$-theory. The renormalization proofs are…
The Hamiltonian of 2+1 dimensional Yang Mills theory was derived by Karabali, Kim and Nair by using point splitting regularization. But in calculating e.g. the vacuum wave functional this scheme was left in favour of arguments. Here we…
It is noted that a given pairing of the phase factor and gauge transformation to retain gauge symmetry is not unique. In their seminal paper, when Yang and Mills (YM) discuss the phase factor - gauge transformation relationship, they cite…
We derive a new functional renormalization group equation for Hamiltonian Yang-Mills theory in Coulomb gauge. The flow equations for the static gluon and ghost propagators are solved under the assumption of ghost dominance within different…
We perform the step-scaling investigation of the running coupling constant, using the gradient-flow scheme, in SU(3) gauge theory with twelve massless fermions in the fundamental representation. The Wilson plaquette gauge action and…
This paper corrects an error in the authors' earlier work, by proving stronger forms of the basic lemmas
Given a compact three-manifold together with a Riemannian metric, we prove the short-time existence of a solution to the renormalization group flow, truncated at the second order term, under a suitable hypothesis on the sectional curvature…
It is shown that in the SU(2) Yang - Mills - Higgs theory with broken gauge symmetry a flux tube solution filled with a color longitudinal electric field exists. The origin of the gauge symmetry breakdown for this case is discussed.