Branes and N=2 Theories in Two Dimensions

TL;DR

This paper uses brane configurations to construct and analyze N=2 supersymmetric gauge theories in two dimensions, revealing deep connections with four-dimensional theories and providing insights into solitons and dualities.

Contribution

It introduces a brane-based framework for studying 2D N=2 theories, linking them to 4D moduli spaces and exploring non-perturbative effects like solitons and dualities.

Findings

Realized quantum properties of sigma models via M theory.

Identified BPS solitons as membrane excitations.

Linked level-rank duality to brane continuation.

Abstract

Type IIA brane configurations are used to construct N=2 supersymmetric gauge theories in two dimensions. Using localization of chiral multiplets in ten-dimensional spacetime, supersymmetric non-linear sigma models with target space such as $\CP^{n-1}$ and the Grassmann manifolds are studied in detail. The quantum properties of these models are realized in $M$ theory by taking the strong Type IIA coupling limit. The brane picture implies an equivalence between the parameter space of N=2 supersymmetric theories in two dimensions and the moduli space of vacua of N=2 supersymmetric gauge theories in four dimensions. Effects like level-rank duality are interpreted in the brane picture as continuation past infinite coupling. The BPS solitons of the $\CP^{n-1}$ model are identified as topological excitations of a membrane and their masses are computed. This provides the brane realization of higher rank tensor representations of the flavor group.