arXiv subjects

N. Nekrasov

Publications and source records attributed to N. Nekrasov.

23 records · Page 2Linked to original sources

arXiv1998

On Conformal Theories in Four Dimensions

Extending recent work of Kachru and Silverstein, we consider ``orbifolds'' of 4-dimensional $\mathcal{N}=4$ SU(n) super-Yang-Mills theories with respect to discrete subgroups of the SU(4) $R$-symmetry which act nontrivially on the gauge group. We show that for every discrete subgroup of SU(4) there is a canonical choice of imbedding of the discrete group in the gauge group which leads to theories with a vanishing one-loop beta-function. We conjecture that these give rise to (generically non-supersymmetric) conformal theories. The gauge group is $\otimes_i SU(Nn_i)$ where $n_i$ denote the dimension of the irreducible representations of the corresponding discrete group; there is also bifundamental matter, dictated by associated quiver diagrams. The interactions can also be read off from the quiver diagram. For SU(3) and SU(2) subgroups this leads to superconformal theories with $\mathcal{N}=1$ and $\mathcal{N}=2$ respectively. In the $\mathcal{N}=1$ case we prove the vanishing of the beta functions to two loops.

hep-th↗

arXiv1998

Chern-Simons and Twisted Supersymmetry in Higher Dimensions

We describe special supersymmetric gauge theories in three, five, seven and nine dimensions, whose compactification on two-, four-, six- and eight-folds produces a supersymmetric quantum mechanics on moduli spaces of holomorphic bundles and/or solutions to the analogues of instanton equations in higher dimensions. The theories may occur on the worldvolumes of D-branes wrapping manifolds of special holonomy. We also discuss the theories with matter.

hep-th↗

arXiv1995

Central Extensions of Gauge Groups Revisited

We present an explicit construction for the central extension of the group $\Map(X, G)$ where $X$ is a compact manifold and $G$ is a Lie group. If $X$ is a complex curve we obtain a simple construction of the extension by the Picard variety $\Pic(X)$. The construction is easily adapted to the extension of $\Aut(E)$, the gauge group of automorphisms of a nontrivial vector bundle $E$.

hep-th↗

arXiv1995

Four-Dimensional Avatars of Two-Dimensional RCFT

We investigate a 4D analog of 2D WZW theory. The theory turns out to have surprising finiteness properties and an infinite-dimensional current algebra symmetry. Some correlation functions are determined by this symmetry. One way to define the theory systematically proceeds by the quantization of moduli spaces of holomorphic vector bundles over algebraic surfaces. We outline how one can define vertex operators in the theory. Finally, we define four-dimensional ``conformal blocks'' and present an analog of the Verlinde formula.

hep-th↗

arXiv1993

Hamiltonian systems of Calogero type and two dimensional Yang-Mills theory

We obtain integral representations for the wave functions of Calogero-type systems,corresponding to the finite-dimentional Lie algebras,using exact evaluation of path integral.We generalize these systems to the case of the Kac-Moody algebras and observe the connection of them with the two dimensional Yang-Mills theory.We point out that Calogero-Moser model and the models of Calogero type like Sutherland one can be obtained either classically by some reduction from two dimensional Yang-Mills theory with appropriate sources or even at quantum level by taking some scaling limit.We investigate large k limit and observe a relation with Generalized Kontsevich Model.

hep-th↗