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N=1 Supersymmetric Gauge Theories and Supersymmetric 3-cycles

Andreas Karch, Dieter Lust, Andre Miemiec

Abstract

In this paper we discuss the strong coupling limit of chiral N=1 supersymmetric gauge theory via their embedding into M-theory. In particular we focus on the brane box models of Hanany and Zaffaroni and show that after a T-duality transformation their M-theory embedding is described by supersymmetric 3-cycles; its geometry will encode the holomorphic non-perturbative information about the gauge theory.

N=1 Supersymmetric Gauge Theories and Supersymmetric 3-cycles

Abstract

In this paper we discuss the strong coupling limit of chiral N=1 supersymmetric gauge theory via their embedding into M-theory. In particular we focus on the brane box models of Hanany and Zaffaroni and show that after a T-duality transformation their M-theory embedding is described by supersymmetric 3-cycles; its geometry will encode the holomorphic non-perturbative information about the gauge theory.

Paper Structure

This paper contains 15 sections, 2 theorems, 81 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. N=2 Gauge Theories and 2-cycles
  3. N=1 Gauge Theories and Supersymmetric 3-cycles
  4. $N=1$ brane boxes
  5. T-duality, M-theory embedding and the emergence of the 3-cycles
  6. Brane Cubes and M-theory
  7. The supersymmetric $d$-cycles
  8. The $d$-cycle equations
  9. Supersymmetric 2-cycles
  10. Supersymmetric 3-cycles
  11. Supersymmetric 3-cycles for intersecting branes and $N=1$ brane boxes
  12. Branes as quaternionic coordinates
  13. Uniform Bending -- Sewing of $N=2$ models
  14. General $N=1$ brane boxes
  15. Conclusions

Key Result

Theorem 1

(Liouville) Suppose $(f^1,\ldots, f^d)$ is a set of smooth functions on a symplectic manifold $M^{2d}$ that are pairwise in involution, i.e. $\{f^i,f^j\}=0$. Let $M_{\xi}$ be the joint level surface determined by a system of equations $f^1(x)=\xi_1,\ldots,f^d(x)=\xi_d$. Suppose the functions are fun

Figures (6)

  • Figure 1: The N=2 brane configuration
  • Figure 2: The N=1 brane configuration
  • Figure 3: Basic cross configuration
  • Figure 5: The intersecting configuration
  • Figure 6: A simple brane box with uniform bending
  • ...and 1 more figures

Theorems & Definitions (4)

  • Definition 1
  • Theorem 1
  • Definition 2
  • Corollary 1