Related papers: Seiberg-Witten Theory and Integrable Systems
This is a general introduction to electric-magnetic duality in non-abelian gauge theories. In chapter I, I review the general ideas which led in the late 70s to the idea of electric/magnetic duality in quantum field theory. In chapters II…
Gauging a discrete 0-form symmetry of a QFT is a procedure that changes the global form of the gauge group but not its perturbative dynamics. In this work, we study the Seiberg-Witten solution of theories resulting from the gauging of…
The quest to reveal the physical essence of the infinitely many symmetries and conservation laws that are intrinsic to integrable systems has historically posed a significant challenge at the confluence of physics and mathematics. This…
The purpose of this paper is twofold. The first purpose is to review a systematic construction of Noether currents for supersymmetric theories, especially effective supersymmetric theories. The second purpose is to use these currents to…
N=2 supersymmetric Yang--Mills theories coupled to matter are considered in the Wess--Zumino gauge. The supersymmetries are realized nonlinearly and the anticommutator between two susy charges gives, in addition to translations, gauge…
Quantum superintegrable systems are solvable eigenvalue problems. Their solvability is due to symmetry, but the symmetry is often "hidden". The symmetry generators of 2nd order superintegrable systems in 2 dimensions close under commutation…
We summarize recent results on the construction of Lax pairs with spectral parameter for the twisted and untwisted elliptic Calogero-Moser systems associated with arbitrary simple Lie algebras, their scaling limits to Toda systems, and…
The application of N=2 supersymmetric quantum mechanics for the quantization of homogeneous systems coupled with gravity is discussed. Starting with the superfield formulation of an N=2 SUSY sigma model, Hermitian self-adjoint expressions…
The new approach to quantum mechanical problems is proposed. Quantum states are represented in an algebraic program, by lists of variable length, while operators are well defined functions on these lists. Complete numerical solution of a…
Recently, new theoretical ideas have allowed the construction of lattice actions which are explicitly invariant under one or more supersymmetries. These theories are local and free of doublers and in the case of Yang-Mills theories also…
We give a full list of known $\mathcal{N}=1$ supersymmetric quantum field theories related by the Seiberg electric-magnetic duality conjectures for $SU(N), SP(2N)$ and $G_2$ gauge groups. Many of the presented dualities are new, not…
We continue the study of the supersymmetric vector multiplet in a purely quantum framework. We obtain some new results which make the connection with the standard literature. First we construct the one-dimensional physical Hilbert space…
In this contribution to the review on localization in gauge theories we investigate the matrix models derived from localizing N=1 super Yang-Mills on S^5. We consider the large-N limit and attempt to solve the matrix model by a saddle-point…
This lecture series consists of mostly independent three parts: Part 1: a tour of basic 4d N=1 supersymmetric dynamics, covering the pure super Yang-Mills, the Seiberg duality for classical groups, the supersymmetric index on S^3, and the…
In these lectures we discuss various aspects of gauge theories with extended $N=2$ and $N=4$ supersymmetry that are at the basis of recently found exact results. These results include the exact calculation of the low energy effective action…
We study four dimensional N=2 G_2 supersymmetric gauge theory on R^3\times S^1 deformed by a tree level superpotential. We will show that the exact superpotential can be obtained by making use of the Lax matrix of the corresponding…
We derive the planar large N non-supersymmetric background of the quantum mechanical hamiltonian of two hermitean matrices coupled via a Yang-Mills interaction, in terms of the density of eigenvalues of one of the matrices. This background…
We present a review of supersymmetry, supergravity, and the non-perturbative dynamics of gauge theories, tracing a path from the supersymmetry algebra to moduli stabilisation and de~Sitter vacua in string theory. Representations of the…
Attempts to solve Yang-Mills theory must eventually face the problem of analyzing the theory at intermediate values of the coupling constant. In this regime neither perturbation theory nor the gravity dual are adequate, and one must…
We establish a new non-minimal Einstein-Yang-Mills-dilaton model, for which the Lagrangian is linear in the curvature and contains eight arbitrary functions of the scalar (dilaton) field. The self-consistent system of equations for the…