Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Open BPS Wall Crossing and M-theory

Mina Aganagic, Masahito Yamazaki

TL;DR

This work extends the D6-D2-D0 BPS counting to include open sectors from D4-branes on a Lagrangian, showing that open BPS degeneracies are captured by the square of the open topological string partition function in a given chamber. Using an M-theory lift to M5-branes on L and a free Fock-space description of M2 states, the authors derive chamber-dependent open+closed BPS partition functions and connect wall-crossing to the Cecotti–Vafa 2d N=(2,2) framework. They provide explicit open BPS wall-crossing formulas and illustrate them with crystal-melting models, establishing consistency with known closed-sector results and CK-type jumps in open invariants. The paper also clarifies the relationship between open BPS counting, open topological strings, and CV wall-crossing, offering predictions for open BPS invariants and their moduli dependence, and bridging multiple approaches to BPS state counting.

Abstract

Consider the degeneracies of BPS bound states of one D6 brane wrapping Calabi-Yau X with D0 branes and D2 branes. When we include D4-branes wrapping Lagrangian cycle L in addition, D2-branes can end on them. These give rise to new bound states in the d=2, N=(2,2) theory of the D4 branes. We call these "open" BPS states, in contrast to closed BPS states that arise from D-branes without boundaries. Lifting this to M-theory, we show that the generating function is captured by free Fock space spanned by M2-brane particles ending on M5 branes wrapping L. This implies that the open BPS bound states are counted by the square of the open topological string partition function on X, reduced to the corresponding chamber. Our results give new predictions for open BPS invariants and their wall crossing phenomena when we change the open and closed string moduli. We relate our results to the work of Cecotti and Vafa on wall crossing in the two dimensional N=(2,2) theories. The findings from the crystal melting model for the open BPS invariants proposed recently fit well with the M-theory predictions.

Open BPS Wall Crossing and M-theory

TL;DR

This work extends the D6-D2-D0 BPS counting to include open sectors from D4-branes on a Lagrangian, showing that open BPS degeneracies are captured by the square of the open topological string partition function in a given chamber. Using an M-theory lift to M5-branes on L and a free Fock-space description of M2 states, the authors derive chamber-dependent open+closed BPS partition functions and connect wall-crossing to the Cecotti–Vafa 2d N=(2,2) framework. They provide explicit open BPS wall-crossing formulas and illustrate them with crystal-melting models, establishing consistency with known closed-sector results and CK-type jumps in open invariants. The paper also clarifies the relationship between open BPS counting, open topological strings, and CV wall-crossing, offering predictions for open BPS invariants and their moduli dependence, and bridging multiple approaches to BPS state counting.

Abstract

Consider the degeneracies of BPS bound states of one D6 brane wrapping Calabi-Yau X with D0 branes and D2 branes. When we include D4-branes wrapping Lagrangian cycle L in addition, D2-branes can end on them. These give rise to new bound states in the d=2, N=(2,2) theory of the D4 branes. We call these "open" BPS states, in contrast to closed BPS states that arise from D-branes without boundaries. Lifting this to M-theory, we show that the generating function is captured by free Fock space spanned by M2-brane particles ending on M5 branes wrapping L. This implies that the open BPS bound states are counted by the square of the open topological string partition function on X, reduced to the corresponding chamber. Our results give new predictions for open BPS invariants and their wall crossing phenomena when we change the open and closed string moduli. We relate our results to the work of Cecotti and Vafa on wall crossing in the two dimensional N=(2,2) theories. The findings from the crystal melting model for the open BPS invariants proposed recently fit well with the M-theory predictions.

Paper Structure

This paper contains 9 sections, 40 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Closed BPS Wall Crossing and M-theory
  3. Open BPS States and M-theory
  4. Open M2 Branes and the Topological String
  5. Open BPS Wall Crossing and M-theory
  6. Examples
  7. Relation to the Work of Cecotti and Vafa
  8. Review of CecottiVold
  9. Counting of Open BPS States

Figures (1)

  • Figure 1: In the $W$-plane, all the $W_{j_i}$'s are on a single line emanating from $W_i$. $W_k$ is infinitely large, and we cut off the $W$-plane at large radius $\Lambda$, shown here in green.