Anomalous reparametrizations and butterfly states in string field theory

TL;DR

This paper explores the reparametrization symmetries in string field theory, showing how they uniquely identify certain projector states called butterfly states, which are important for understanding D-branes.

Contribution

It demonstrates that reparametrization identities uniquely select butterfly projectors and provides a simple proof of their projector property within regularized vacuum string field theory.

Findings

Reparametrization symmetries uniquely select butterfly projectors.

Butterfly states are proven to be projectors.

Identities constrain surface states in string field theory.

Abstract

The reparametrization symmetries of Witten's vertex in ordinary or vacuum string field theories can be used to extract useful information about classical solutions of the equations of motion corresponding to D-branes. It follows, that the vacuum string field theory in general has to be regularized. For the regularization recently considered by Gaiotto et al., we show that the identities we derive, are so constraining, that among all surface states they uniquely select the simplest butterfly projector discovered numerically by those authors. The reparametrization symmetries are also used to give a simple proof that the butterfly states and their generalizations are indeed projectors.