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Branes and N=2 Theories in Two Dimensions

Amihay Hanany, Kentaro Hori

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.

Branes and N=2 Theories in Two Dimensions

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 and the Grassmann manifolds are studied in detail. The quantum properties of these models are realized in 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 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.

Paper Structure

This paper contains 20 sections, 103 equations, 13 figures.

Table of Contents

  1. Introduction
  2. $N=2$ Theories in Two Dimensions
  3. General Background on $N=2$ SUSY Field Theories
  4. Gauged Linear Sigma Models
  5. The ${\bf C}{\rm P}^{n-1}$ Model
  6. Other $k=1$ Theories
  7. The Grassmannian Model
  8. A Type IIA Configuration
  9. Field Theory on the D2-brane World-volume
  10. Classical Space of Vacua
  11. Quantum Properties Via $M$ Theory
  12. $M$ Theory Description of the Configuration
  13. Quantum Properties of the Theory
  14. The Structure of Vacua
  15. Continuation Past Infinite Coupling
  16. ...and 5 more sections

Figures (13)

  • Figure 1: The Two Paths
  • Figure 2: The IIA configuration for general twisted mass
  • Figure 3: $U(k)$ gauge theory coupled to $n$ chiral multiplets. There are $k$ D2 branes stretched between NS and NS$'$ fivebranes. $n$ semi-infinite (upper) D4 branes end on the NS$'$ fivebrane.
  • Figure 4: Turning on a FI term when the D2 branes are in between the two NS branes. The D2 branes must end on the NS branes to avoid charge violation. As a result their orientation in space-time is changed and thus supersymmetry is broken.
  • Figure 5: A Type IIA description of the exchange of two NS branes. This is a classical transition which is corrected quantum mechanically. In the figure there are D2 branes stretched between infinite D4 branes and a NS brane. The D2 branes are created when the D4 and the NS branes pass each other in the $x^6$ direction.
  • ...and 8 more figures