D-Brane Bound States Redux

TL;DR

This paper investigates the existence of D-brane bound states in Type II string theories, deriving an index theorem and providing evidence supporting conjectures about M-theory and the absence of certain BPS states.

Contribution

It introduces a new index theorem for non-Fredholm operators and demonstrates the existence or non-existence of specific D-brane bound states, supporting key theoretical conjectures.

Findings

Bound state exists for two coincident zero-branes.

No BPS bound states for two and three-branes on Calabi-Yau cycles.

Supports the matrix model description of M-theory.

Abstract

We study the existence of D-brane bound states at threshold in Type II string theories. In a number of situations, we can reduce the question of existence to quadrature, and the study of a particular limit of the propagator for the system of D-branes. This involves a derivation of an index theorem for a family of non-Fredholm operators. In support of the conjectured relation between compactified eleven-dimensional supergravity and Type IIA string theory, we show that a bound state exists for two coincident zero-branes. This result also provides support for the conjectured description of M-theory as a matrix model. In addition, we provide further evidence that there are no BPS bound states for two and three-branes twice wrapped on Calabi-Yau vanishing cycles.