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Phases Of N=2 Theories In 1+1 Dimensions With Boundary

Manfred Herbst, Kentaro Hori, David Page

Abstract

We study B-type D-branes in linear sigma models with Abelian gauge groups. The most important finding is the grade restriction rule. It classifies representations of the gauge group on the Chan-Paton factor, which can be used to define a family of D-branes over a region of the Kähler moduli space that connects special points of different character. As an application, we find a precise, transparent relation between D-branes in various geometric phases as well as free orbifold and Landau-Ginzburg points. The result reproduces and unifies many of the earlier mathematical results on equivalences of D-brane categories, including the McKay correspondence and Orlov's construction.

Phases Of N=2 Theories In 1+1 Dimensions With Boundary

Abstract

We study B-type D-branes in linear sigma models with Abelian gauge groups. The most important finding is the grade restriction rule. It classifies representations of the gauge group on the Chan-Paton factor, which can be used to define a family of D-branes over a region of the Kähler moduli space that connects special points of different character. As an application, we find a precise, transparent relation between D-branes in various geometric phases as well as free orbifold and Landau-Ginzburg points. The result reproduces and unifies many of the earlier mathematical results on equivalences of D-brane categories, including the McKay correspondence and Orlov's construction.

Paper Structure

This paper contains 95 sections, 836 equations, 35 figures.

Table of Contents

  1. Introduction
  2. A guide to read the paper
  3. D-branes In ${\mathcal{N}}=2$ Theories
  4. ${\mathcal{N}}=1$ Supersymmetric Interactions
  5. Brane-Antibrane System And Open String Tachyons
  6. Non-Linear Sigma Models: Complex Of Vector Bundles
  7. Condition Of ${\mathcal{N}}=2$ Supersymmetry
  8. R-Symmetry
  9. Chiral Sector
  10. Orbifolds
  11. Landau-Ginzburg Models: Matrix Factorizations
  12. Landau-Ginzburg Orbifold
  13. Renormalization Group Flows
  14. D-Term Deformations And Brane-Antibrane Annihilation
  15. Binding D-Branes: Cone Construction
  16. ...and 80 more sections

Figures (35)

  • Figure 1: The Phases of the model (A) for $N=5$.
  • Figure 2: The Phases of the model (B).
  • Figure 3: The Phases of the two parameter model (C).
  • Figure 4: The Amoeba (Left) and Alga (Right) of $\mathfrak{S}$ of the two parameter model (C).
  • Figure 5: The exceptional divisor of the resolved $A_{N-1}$ singularity.
  • ...and 30 more figures