Wedge states in string field theory

TL;DR

This paper explores the algebraic properties of wedge states in string field theory, introducing new expressions and analyzing their behavior, especially regarding associativity and convergence in level truncation methods.

Contribution

It presents a novel algebraic expression for wedge states, examines their matter and ghost sectors separately, and studies their role in convergence and anomalies in string field algebra.

Findings

New algebraic expression for wedge states

Wedge states with different matter and ghost parts violate associativity

Wedge states with insertions help analyze convergence and anomalies

Abstract

The wedge states form an important subalgebra in the string field theory. We review and further investigate their various properties. We find in particular a novel expression for the wedge states, which allows to understand their star products purely algebraically. The method allows also for treating the matter and ghost sectors separately. It turns out, that wedge states with different matter and ghost parts violate the associativity of the algebra. We introduce and study also wedge states with insertions of local operators and show how they are useful for obtaining exact results about convergence of level truncation calculations. These results help to clarify the issue of anomalies related to the identity and some exterior derivations in the string field algebra.