相关论文: $\ast$-SDYM Fields and Heavenly Spaces. I. $\ast$-…
We describe an infinite-dimensional Kac-Moody-Virasoro algebra of new hidden symmetries for the self-dual Yang-Mills equations related to conformal transformations of the 4-dimensional base space.
We define a natural generalized symmetry of the Yang-Mills equations as an infinitesimal transformation of the Yang-Mills field, built in a local, gauge invariant, and Poincar\'e invariant fashion from the Yang-Mills field strength and its…
Solutions of Hitchin's self-duality equations corresponds to special real sections in the Deligne-Hitchin moduli space -- twistor lines. A question posed by Simpson in 1997 asks whether all real sections give rise to global solutions of the…
In harmonic superspace, the classical equations of motion of $D=4, N=2$ supersymmetric Yang-Mills theory for Minkowski and Euclidean spaces are analyzed. We study dual superfield representations of equations and subsidiary conditions…
We consider the classical self-dual Yang-Mills equation in 3+1-dimensional Minkowski space. We have found an exact solution, which describes scattering of $n$ plane waves. In order to write the solution in a compact form, it is convenient…
We introduce a new point of view to present classical notions related to set-theoretic solutions of the Yang-Baxter equation: left skew braces, dirings, left skew rings. The idea is to replace the single multiplication on a left near-ring…
This is a next paper from a sequel devoted to algebraic aspects of Yang-Mills theory. We undertake a study of deformation theory of Yang-Mills algebra YM - a ``universal solution'' of Yang-Mills equation. We compute (cyclic) (co)homology of…
Physically relevant gauge and gravitational theories can be seen as special members of hierarchies of more elaborate systems. The Yang-Mills (YM) system is the first member of a hierarchy of Lagrangians which we will index by $p_1$, and the…
The anti-self-dual Yang-Mills equations are known to have reductions to many integrable differential equations. A general B\"acklund transformation (BT) for the ASDYM equations generated by a Darboux matrix with an affine dependence on the…
We show how matter can be included in a constrained ADM-like formulation of the Einstein equations on constant mean curvature surfaces. Previous results on the regularity of the equations at future null infinity are unaffected by the…
From a study of the subleading structure of the asymptotic equations of motion in Einstein-Yang-Mills theory, we construct charges that are conserved up to quadratic order in non-radiative vacuum. We then show that these higher spin charges…
The conformal field equations are used to discuss the local existence of spherically symmetric solutions to the Einstein-Yang-Mills system which behave asymptotically like the anti-de Sitter spacetime. By using a gauge based on conformally…
New solutions to the static, spherically symmetric Einstein-Yang-Mills-Higgs equations with the Higgs field in the triplet resp. doublet representation are presented. They form continuous families parametrized by $\alpha=M_W/M_Pl$ ($M_W$…
We study the space of periodic solutions of the elliptic $\sinh$-Gordon equation by means of spectral data consisting of a Riemann surface $Y$ and a divisor $D$. We show that the space $M_g^{\mathbf{p}}$ of real periodic finite type…
We analyze the constraints for a system of anti self-dual Yang-Mills (ASDYM) equations by means of the modified Faddeev-Jackiw method in K and J gauges \`{a} la Yang. We also establish the Hamiltonian flow for ASDYM system through the…
It is known for ten years that self-dual Yang-Mills theory is the effective field theory of the open N=2 string in 2+2 dimensional spacetime. We uncover an infinite set of abelian rigid string symmetries, corresponding to the symmetries and…
We study the twisted ampleness criterion due to Collins, Jacob and Yau on surfaces, which is equivalent to the existence of solutions to the deformed Hermitian-Yang-Mills (dHYM) equation. When $X$ is a Weierstrass elliptic K3 surface, and…
The exact quantum integrability aspects of a sector of the membrane is investigated. It is found that spherical membranes moving in flat target spacetime backgrounds admit a class of integrable solutions linked to SU(infty) SDYM equations…
We discuss infinite-dimensional hidden symmetry algebras (and hence an infinite number of conserved nonlocal charges) of the N-extented self-dual super Yang-Mills equations for general N\leq4 by using the supertwistor correspondence.…
We show the existence of Yang--Mills--Higgs (YMH) fields over a Riemann surface with boundary where a free boundary condition is imposed on the section and a Neumann boundary condition on the connection. In technical terms, we study the…