The singular geometry of the sliver

TL;DR

This paper analyzes the geometric and algebraic properties of sliver states in string field theory, revealing their singular nature and potential role in describing D-branes and closed strings.

Contribution

It characterizes the singular geometry of sliver states and explores their algebraic structure, especially in the zero slope limit, linking open and closed string descriptions.

Findings

Sliver states are singular projection operators in string field theory.

In the zero slope limit, the star algebra simplifies to a product of space-time functions and noncommutative fields.

The geometric analogy of the sliver provides insights into closed string state descriptions.

Abstract

We consider "sliver" states which act as projection operators in the matter star product of Witten's cubic string field theory. These sliver states, which might be associated with Dirichlet p-branes, are not finite norm states in the matter string Hilbert space. We describe the singularities of these states, and demonstrate that the sliver states are composed of strings having singular geometric features. These singularities take a particularly simple form in the zero slope limit alpha' -> 0, where the star algebra factorizes into a product of the algebra of functions on space-time and the noncommutative star product of fields associated with higher string modes. An analogy to the sliver geometry suggests a natural mechanism for describing closed string states in open string field theory.