Identity Projector and D-brane in String Field Theory

TL;DR

This paper explores the role of identity projectors in string field theory, linking them to noncommutative geometry and boundary entropy, revealing their connection to D-brane tension.

Contribution

It introduces a novel interpretation of identity projectors as projectors in noncommutative geometry, relating their trace to boundary entropy and D-brane tension.

Findings

Identity projectors correspond to projectors in the linking algebra.

The regularized trace of these projectors equals boundary entropy.

Boundary entropy is proportional to D-brane tension.

Abstract

We study the identity projectors of the string field theory in the generic BCFT background. We explain how it can be identified as the projector in the linking algebra of the noncommutative geometry. We show that their (regularized) trace is exactly given by the boundary entropy which is proportional to the D-brane tension.