D-Branes and Spin^c Structures

TL;DR

This paper investigates the Spin^c structure requirement for D-branes in string theory, demonstrating that in certain compactifications, the normal bundle to supersymmetric cycles naturally admits a Spin^c structure, ensuring consistency.

Contribution

It shows that in type II string compactifications with zero cosmological constant, the normal bundle to supersymmetric cycles inherently possesses a Spin^c structure, confirming Witten's constraint.

Findings

Normal bundle to supersymmetric cycles is automatically Spin^c in these compactifications.

Supports Witten's condition for D-brane consistency.

Provides geometric insight into D-brane wrapping conditions.

Abstract

It was recently pointed out by E. Witten that for a D-brane to consistently wrap a submanifold of some manifold, the normal bundle must admit a Spin^c structure. We examine this constraint in the case of type II string compactifications with vanishing cosmological constant, and argue that in all such cases, the normal bundle to a supersymmetric cycle is automatically Spin^c.