Related papers: Generalized WDVV equations for B_r and C_r pure N=…
An associative algebra of holomorphic differential forms is constructed associated with pure N=2 Super-Yang-Mills theory for the Lie algebra F4. Existence and associativity of this algebra, combined with the general arguments in the work of…
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…
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…
This paper studies the dual form of Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations in N=2 supersymmetric Yang-Mills theory by applying a duality transformation to WDVV equations. The dual WDVV equations called in this paper are…
It is well-known that the perturbative prepotentials of four-dimensional N=2 supersymmetric Yang-Mills theories satisfy the generalized WDVV equations, regardless of the gauge group. In this paper we study perturbative prepotentials of the…
Prepotentials in N=2 supersymmetric Yang-Mills theories are known to obey non-linear partial differential equations called Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. In this paper, the prepotentials at one-instanton level in N=2…
A two dimensional gauge theory is canonically associated to every Drinfeld double. For particular doubles, the theory turns out to be e.g. the ordinary Yang-Mills theory, the G/G gauged WZNW model or the Poisson $\sigma$-model that…
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…
A class of solutions to the WDVV equations is provided by period matrices of hyperelliptic Riemann surfaces, with or without punctures. The equations themselves reflect associativity of explicitly described multiplicative algebra of…
A noncommutative version of the (anti-) self-dual Yang-Mills equations is shown to be related via dimensional reductions to noncommutative formulations of the generalized (SO(3)/SO(2)) nonlinear Schrodinger (NS) equations, of the…
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…
The prepotential $F(a_i)$, defining the low-energy effective action of the $SU(N)$ ${\cal N}=2$ SUSY Yang-Mills theories, satisfies an enlarged set of the WDVV-like equations $F_iF_k^{-1}F_j = F_jF_k^{-1}F_i$ for any triple $i,j,k =…
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…
We construct second order reductions of the generalized Witten-Dijkgraaf-Verlinde-Verlinde system based on simple Lie algebras. We discuss to what extent some of the symmetries of the WDVV system are preserved by the reduction.
The Lie algebra $\mathcal{D}$ of regular differential operators on the circle has a universal central extension $\hat{\mathcal{D}}$. The invariant subalgebra $\hat{\mathcal{D}}^+$ under an involution preserving the principal gradation was…
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…
N=4 superconformal n-particle quantum mechanics on the real line is governed by two prepotentials, U and F, which obey a system of partial nonlinear differential equations generalizing the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation.…
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…
We consider the prepotential of Dijkgraaf and Vafa (DV) as one more (and in fact, singular) example of the Seiberg-Witten (SW) prepotentials and discuss its properties from this perspective. Most attention is devoted to the issue of…
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…