Related papers: Generalized WDVV equations for F4 pure N=2 Super-Y…
A proof that the prepotential for pure N=2 Super-Yang-Mills theory associated with Lie algebras B_r and C_r satisfies the generalized WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) system was given by Marshakov, Mironov and Morozov. Among other…
We present a simple proof of the WDVV equations for the prepotential of four-dimensional N=2 supersymmetric Yang-Mills theory with all ADE gauge groups. According to our proof it is clearly seen that the WDVV equations in four dimensions…
We consider 4d and 5d N=2 supersymmetric theories and demonstrate that in general their Seiberg-Witten prepotentials satisfy the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. General proof for the Yang-Mills models (with matter in…
Recently Alday, Gaiotto and Tachikawa have proposed relation between 2- and 4-dimensional conformal field theories. The relation implies that the Nekrasov partition functions of N=2 superconformal gauge theories are equal to conformal…
We formulate noncommutative self-dual N=4 supersymmetric Yang-Mills theory in D=2+2 dimensions. As in the corresponding commutative case, this theory can serve as the possible master theory of all the noncommutative supersymmetric…
In the present paper we analyze algebraic structures arising in Yang-Mills theory. The paper should be considered as a part of a project started with a paper "On maximally supersymmetric Yang-Mills theories" devoted to maximally…
After a short introduction on the theory of homogeneous algebras we describe the application of this theory to the analysis of the cubic Yang-Mills algebra, the quadratic self-duality algebras, their "super" versions as well as to some…
Using bootstrap methods, we provide evidence for the existence of a non-linear W-algebra, denoted $W_\infty^\text{s,s}$, which contains the small N= 4 super Virasoro algebra and features an infinite tower of additional generators, organized…
We will discuss an integrable structure for weakly coupled superconformal Yang-Mills theories, describe certain equivalences for the Yangian algebra, and fill a technical gap in our previous study of this subject.
We present a series of four self-contained lectures on the following topics: (I) An introduction to 4-dimensional 1\leq N \leq 4 supersymmetric Yang-Mills theory, including particle and field contents, N=1 and N=2 superfield methods and the…
We construct the $N=2$ super $W_4$ algebra as a certain reduction of the second Gel'fand-Dikii bracket on the dual of the Lie superalgebra of $N=1$ super pseudo-differential operators. The algebra is put in manifestly $N=2$ supersymmetric…
The Seiberg-Witten curves and differentials for $\N=2$ supersymmetric Yang-Mills theories with one hypermultiplet of mass $m$ in the adjoint representation of the gauge algebra $\G$, are constructed for arbitrary classical or exceptional…
We perform dimensional reductions of recently constructed self-dual $~N=2$~ {\it supersymmetric} Yang-Mills theory in $~2+2\-$dimensions into two-dimensions. We show that the universal equations obtained in these dimensional reductions can…
The Yang-Mills equations are formulated in the form of generalized Maurer-Cartan equations, such that the corresponding algebraic operations are shown to satisfy the defining relations of homotopy Lie superalgebra.
We derive the $N=2$ and $4$ super Yang-Mills theories from the viewpoint of the $M_4\times Z_2\times Z_2$ gauge theory. Scalars and pseudoscalars appearing in the theories are regarded as gauge fields along the directions on $Z_2\times Z_2$…
We show that recently formulated four-dimensional self-dual supersymmetric Yang-Mills theory, which is consistent background for open $~N=2$~ superstring, generates two-dimensional $~N=(1,1),~\, N=(1,0) $~ and $~N=(2,0)$~ supersymmetric…
Electromagnetism can be generalized to Yang-Mills theory by replacing the group U(1)$ by a nonabelian Lie group. This raises the question of whether one can similarly generalize 2-form electromagnetism to a kind of "higher-dimensional…
We review the relation of N=4 superconformal multi-particle models on the real line to the WDVV equation and an associated linear equation for two prepotentials, F and U. The superspace treatment gives another variant of the integrability…
A solution to Slavnov-Taylor identities in a general four dimensional N=1 supersymmetric Yang-Mills theory containing arbitrary matter superfields is proposed. The solution proposed appears just a simple generalization of an analogous…
Four dimensional N=1 supersymmetric Yang-Mills theory action is written in terms of the spinor superfields in transverse gauge. This action is seemingly first order in space-time derivatives. Thus, it suggests that the generalized fields…