Squeezed State Projectors in String Field Theory

TL;DR

This paper identifies a new subalgebra of squeezed states in string field theory, including projectors like the sliver and butterfly states, facilitating analysis of their spectra and enabling multi D-brane constructions.

Contribution

It introduces a novel subalgebra of squeezed states with commuting matrices, encompassing key projectors and allowing spectral analysis and multi D-brane state construction.

Findings

The subalgebra contains the sliver and butterfly states.

Eigenvalues provide a new representation for these states.

Different butterfly states are orthogonal, enabling multi D-brane configurations.

Abstract

We find a new subalgebra of the star product in the matter sector. Its elements are squeezed states whose matrices commute with (K_1)^2. This subalgebra contains a large set of projectors. The states are represented by their eigenvalues and we find a mapping between the eigenvalues representation and other known representations. The sliver is naturally in this subalgebra. Surprisingly, all the generalized butterfly states are also in this subalgebra, enabling us to analyze their spectrum, and to show the orthogonality of different butterfly states. This means that multi D-brane states can be built of butterfly states.