Comma Vertex and String Field Algebra

TL;DR

This paper investigates the algebraic structure of open string fields using a novel 'comma vertex' approach, deriving a general form for N-string vertices and exploring their connection to wedge states in string field theory.

Contribution

It introduces the 'comma vertex' for the matter part of open string field algebra and generalizes it to N-string overlaps, providing a closed form for Neumann coefficients.

Findings

Derived a closed form of Neumann coefficients for N-string vertices.

Connected the N-string vertex to the oscillator representation of wedge states.

Enhanced understanding of the algebraic structure of open string fields.

Abstract

We study the matter part of the algebra of open string fields using the 3-string vertex over the sliver state, which we call ``comma vertex''. By generalizing this comma vertex to the $N$-string overlap, we obtain a closed form of the Neumann coefficients in the $N$-string vertex and discuss its relation to the oscillator representation of wedge states.