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Some Navigation Rules for D-Brane Monodromy

Paul S. Aspinwall

Abstract

We explore some aspects of monodromies of D-branes in the Kahler moduli space of Calabi-Yau compactifications. Here a D-brane is viewed as an object of the derived category of coherent sheaves. We compute all the interesting monodromies in some nontrivial examples and link our work to recent results and conjectures concerning helices and mutations. We note some particular properties of the 0-brane.

Some Navigation Rules for D-Brane Monodromy

Abstract

We explore some aspects of monodromies of D-branes in the Kahler moduli space of Calabi-Yau compactifications. Here a D-brane is viewed as an object of the derived category of coherent sheaves. We compute all the interesting monodromies in some nontrivial examples and link our work to recent results and conjectures concerning helices and mutations. We note some particular properties of the 0-brane.

Paper Structure

This paper contains 13 sections, 35 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Autoequivalences and the Fourier-Mukai Transform
  3. A One Parameter Case
  4. Helices and Mutations
  5. A Two Parameter Case
  6. $C_1$
  7. $C_2$
  8. $C_3$
  9. $C_4$
  10. Other Examples
  11. Surfaces shrinking to curves
  12. A reducible exceptional divisor
  13. Discussion of the 0-Brane

Figures (4)

  • Figure 1: The 4 phases of the 2 parameter example.
  • Figure 2: The moduli space ${\Scr M}$.
  • Figure 3: The triply linked circles.
  • Figure 4: The ${\mathbb C}^2/{\mathbb Z}_3$ resolution phase space.

Theorems & Definitions (3)

  • Conjecture 1
  • Conjecture 2
  • Conjecture 3