相关论文: WDVV Equations and Seiberg-Witten theory
This is a short review of the results on the associativity algebras and WDVV equations found recently for the Seiberg-Witten solutions of N=2 4d SUSY gauge theories. The presentation is mostly based on the integrable treatment of these…
The properties of the N=2 SUSY gauge theories underlying the Seiberg-Witten hypothesis are discussed. The main ingredients of the formulation of the finite-gap solutions to integrable equations in terms of complex curves and generating…
We consider the associativity (or WDVV) equations in the form they appear in Seiberg-Witten theory and prove that they are covariant under generic electric-magnetic duality transformations. We discuss the consequences of this covariance…
We present a complete proof that solutions of the WDVV equations in Seiberg-Witten theory may be constructed from root systems. A generalization to weight systems is proposed.
This note gives a brief review of the integrable structures presented in the Seiberg-Witten approach to the N=2 SUSY gauge theories with emphasize on the case of the gauge theories with matter hypermultiplets included (described by spin…
A summary of results is presented, which provide exact description of the low-energy $4d$ $N=2$ and $N=4$ SUSY gauge theories in terms of $1d$ integrable systems.
The role of associativity or WDVV equations in effective supersymmetric quantum theories is discussed and it is demonstrated that for wide class of their solutions when residue formulas are valid the proof of associativity equations can be…
These lectures are devoted to the low energy limit of \N2 SUSY gauge theories, which is described in terms of integrable systems. A special emphasis is on a duality that naturally acts on these integrable systems. The duality turns out to…
We consider the associativity or Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations and discuss one of the most relevant for non-perturbative physics class of their solutions based on existence of the residue formulas. It is demonstrated…
It is known that electric-magnetic duality transformations are symmetries of the generalized Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. In Seiberg-Witten theory the solutions to these equations come in certain sets according to…
In this note it is demonstrated how the Seiberg-Witten solutions and related integrable systems may arise from certain brane configurations in M-theory. Some subtleties of the formulation of the Seiberg-Witten theory via integrable systems…
We propose a few tests of Seiberg-Witten solutions of $\mathcal{N}=2$ supersymmetric gauge theories by the instanton calculus in twisted gauge theories. We re-examine the low-energy effective abelian theory in the presence of sources and…
Seiberg-Witten solutions of four-dimensional supersymmetric gauge theories possess rich but involved integrable structures. The goal of this paper is to show that an isomonodromy problem provides a unified framework for understanding those…
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…
We review the Seiberg-Witten construction of low-energy effective actions and BPS spectra in SUSY gauge theories and its formulation in terms of integrable systems. It is also demonstrated how this formulation naturally appears from the…
We briefly review the Whitham hierarchies and their applications to integrable systems of the Seiberg-Witten type. The simplest example of the N=2 supersymmetric SU(2) pure gauge theory is considered in detail and the corresponding Whitham…
The Seiberg-Witten solution plays a central role in the study of N=2 supersymmetric gauge theories. As such, it provides a proving ground for a wide variety of techniques to treat such problems. In this review we concentrate on the role of…
We study the generalized matrix model which corresponds to the n-point toric Virasoro conformal block. This describes four-dimensional N=2 SU(2)^n gauge theory with circular quiver diagram by the AGT relation. We first verify that it is…
We consider the Seiberg-Witten Toda chains arising in the context of exact solutions to N=2 SUSY Yang-Mills and their relation to the properties of N=1 SUSY gauge theories. In particular, we discuss their "perturbative" and "solitonic"…
The (generalized) WDVV equations for the prepotentials in $2d$ topological and $4,5d$ Seiberg-Witten models are covariant with respect to non-linear transformations, described in terms of solutions of associated linear problem. Both…