Related papers: Integrability and Seiberg-Witten Exact Solution

Motivated by the idea that consistent quantum field theories should admit a finite description, we investigate the complexity of effective field theories using the framework of effective o-minimality. Our focus is on quantifying the…

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…

In view of two-dimensional topological gravity coupled to matter, we study the Seiberg-Witten theory for the low-energy behavior of N=2 supersymmetric Yang-Mills theory with ADE gauge groups. We construct a new solution of the Picard-Fuchs…

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…

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…

Review of the theory of effective actions and the hypothetical origins of integrability in Seiberg-Witten theory.

We consider the Yang-Mills equations with a matrix gauge group $G$ on the de Sitter dS$_4$, anti-de Sitter AdS$_4$ and Minkowski $R^{3,1}$ spaces. On all these spaces one can introduce a doubly warped metric in the form $d s^2 =-d u^2 + f^2…

We investigate integrability properties of Gukov-Witten 1/2-BPS surface defects in $SU(N)$ $\mathcal{N}=4$ super-Yang-Mills (SYM) theory in the large-$N$ limit. We demonstrate that ordinary Gukov-Witten defects, which depend on a set of…

An elementary introduction into the Seiberg-Witten theory is given. Many efforts are made to get it as pedagogical as possible, within a reasonable size. The selection of the relevant material is heavily oriented towards graduate students.…

Gorsky et al. presented an explicit construction of Whitham deformations of the Seiberg-Witten curve for the $SU(N+1)$ $\calN = 2$ SUSY Yang-Mills theory. We extend their result to all classical gauge groups and some other cases such as the…

In the mid 1990's Seiberg and Witten determined the exact low energy effective action of $\mathcal{N}=2$ supersymmetric Yang-Mills theory with gauge group $SU(2)$. Later, in the early 2000's Nekrasov calculated this action directly using…

The n-instanton contribution to the Seiberg-Witten prepotential of N=2 supersymmetric d=4 Yang Mills theory is represented as the integral of the exponential of an equivariantly exact form. Integrating out an overall scale and a U(1) angle…

A reliable method to construct Supersymmetric Noether currents is presented. As the most important application the central charge of the N=2 Supersymmetric Yang-Mills effective theory, known as Seiberg-Witten (SW) theory, is computed. The…

The exact quantum integrability problem of the membrane is investigated. It is found that the spherical membrane moving in flat target spacetime backgrounds is an exact quantum integrable system for a particular class of solutions of the…

We study N=2 super Yang-Mills theory with gauge group SU(N) from the point of view of the Whitham hierarchy. We develop a new recursive method to compute the whole instanton expansion of the prepotential using the theta function associated…

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…

We consider a Yang-Mills type gauge theory of gravity based on the conformal group SO(4,2) coupled to a conformally invariant real scalar field. The goal is to generate fundamental dimensional constants via spontaneous breakdown of the…

The one-loop dilatation operator in Yang-Mills theory possesses a hidden integrability symmetry in the sector of maximal helicity Wilson operators. We calculate two-loop corrections to the dilatation operator and demonstrate that while…

We solve N=2 supersymmetric Yang-Mills theories for arbitrary classical gauge group, i.e. SU(N), SO(N), Sp(N). In particular, we derive the prepotential of the low-energy effective theory, and the corresponding Seiberg-Witten curves. We…

We present exact solutions in Einstein-Yang-Mills-Dirac theories with gauge groups SU(2) and SU(4) in Robertson-Walker space-time $R \times S^3 $, which are symmetric under the action of the group SO(4) of spatial rotations. Our approach is…