Star Algebra Projectors

TL;DR

This paper classifies a broad class of surface state projectors in open string field theory, revealing their geometric properties, invariances, and specific examples like the butterfly and nothing states.

Contribution

It introduces a general class of star algebra projectors derived from surface states with boundary-reaching midpoints, expanding understanding of string field configurations.

Findings

Surface states with boundary-reaching midpoints form a class of projectors.

All such projectors are invariant under certain half-string translations.

Identifies specific projectors including the butterfly and nothing states.

Abstract

Surface states are open string field configurations which arise from Riemann surfaces with a boundary and form a subalgebra of the star algebra. We find that a general class of star algebra projectors arise from surface states where the open string midpoint reaches the boundary of the surface. The projector property of the state and the split nature of its wave-functional arise because of a nontrivial feature of conformal maps of nearly degenerate surfaces. Moreover, all such projectors are invariant under constant and opposite translations of their half-strings. We show that the half-string states associated to these projectors are themselves surface states. In addition to the sliver, we identify other interesting projectors. These include a butterfly state, which is the tensor product of half-string vacua, and a nothing state, where the Riemann surface collapses.