相关论文: Complex Burgers' equation in 2D SU(N) YM

We calculate the exact values of the holomorphic observables of {\cal N}=4 supersymmetric SU(N) Yang-Mills theory deformed by mass terms which preserve {\cal N}=1 SUSY. These include the chiral condensates in each massive vacuum of the…

The equations for a self-similar solution of an inviscid incompressible fluid are mapped into an integral equation which hopefully can be solved by iteration. It is argued that the exponent of the similarity are ruled by Kelvin's theorem of…

We consider free surface dynamics of a two-dimensional incompressible fluid with odd viscosity. The odd viscosity is a peculiar part of the viscosity tensor which does not result in dissipation and is allowed when parity symmetry is broken.…

Compact string expressions are found for non-intersecting Wilson loops in SU(N) Yang-Mills theory on any surface (orientable or nonorientable) as a weighted sum over covers of the surface. All terms from the coupled chiral sectors of the…

We study $\frac{1}{4}$-BPS Wilson loops in four-dimensional SU$(N$) ${\mathcal{N}}=2$ super-Yang-Mills theories with conformal matter in an arbitrary representation $\mathcal{R}$. These operators are formed of two meridians on the…

The prepotential and spectral curve are described for a smooth interpolation between an enlarged N=4 SUSY and ordinary N=2 SUSY Yang-Mills theory in four dimensions, obtained by compactification from five dimensions with non-trivial…

In recent years it has been shown that many, and possibly all, integrable systems can be obtained by dimensional reduction of self-dual Yang-Mills. I show how the integrable systems obtained this way naturally inherit bihamiltonian…

The dynamics of Wilson loops are governed by an infinite set of Schwinger-Dyson equations and trace relations. In the context of the lattice positivity bootstrap, a central challenge is determining a dynamically independent basis of these…

We consider $SU(N)$ Yang-Mills theories in $(2n+1)$-dimensional Euclidean spacetime, where $N\geq n+1$, coupled to an even flavour number of Dirac fermions. After integration over the fermionic degrees of freedom the wave functional for the…

Gathering together some existing results, we show that the solutions to the one-dimensional Burgers equation converge for long times towards the stationary solutions to the steady Burgers equation, whose Fourier spectrum is not integrable.…

Yang Mills theory in 2+1 dimensions can be expressed as an array of coupled (1+1)-dimensional principal chiral sigma models. The $SU(N)\times SU(N)$ principal chiral sigma model in 1+1 dimensions is integrable, asymptotically free and has…

We study the low-energy dynamics of noncommutative $\N=2$ supersymmetric U(N) Yang-Mills theories in the Coulomb phase. Exact results are derived for the leading terms in the derivative expansion of the Wilsonian effective action. We find…

It is shown that the $SU(2)$ Yang-Mills theory in $3$-dimensional Riemann-Cartan space-time can be completely reformulated as a gravity-like theory in terms of gauge invariant variables. The resulting Yang-Mills induced equations are found,…

We discuss the Seiberg-Witten solution of the non-commutative N=2 U(N) SYM model. The solution is described in terms of the ordinary Seiberg-Witten curve of the SU(N) theory plus an additional free U(1). Hence, at the two-derivative…

We consider weakly asymmetric exclusion processes whose initial density profile is a small perturbation of a constant. We show that in the diffusive time-scale, in all dimensions, the density defect evolves as the solution of a viscous…

It is presented the general method that allows to formulate 4D $SU(N)$ Yang - Mills theory in terms of only local gauge invariant variables. For the case N=2, that is discussed in details, this gauge invariant formulation appears to be very…

The tube solutions in Yang - Mills - Higgs theory are received, in which the Higgs field has the negative energy density. This solutions make up the discrete spectrum numered by two integer and have the finite linear energy density.…

We give a physical interpretation for the analytic continuation of the partition function of superconformal SU$(2)$ $\mathcal{N}=2$ gauge theory on the four-sphere to all values of the Yang-Mills coupling. We show that a well-motivated 2d…

We provide a constructive global existence proof for the multivariate viscous Burgers equation system defined on the whole space or on a domain isomorphic to the n-torus and with time horizon up to infinity and C^{\infty}- data (satisfying…

Classically, the dual under the Seiberg-Witten map of noncommutative U(N), {\cal N}=1 super Yang-Mills theory is a field theory with ordinary gauge symmetry whose fields carry, however, a \theta-deformed nonlinear realisation of the {\cal…