N-String Vertices in String Field Theory

TL;DR

This paper derives a general mathematical form for the interaction vertex of any number of strings in string field theory, using matrix representations and the comma formalism to unify interactions.

Contribution

It introduces a comprehensive formulation for N-string interaction vertices applicable to any number of strings within the comma representation framework.

Findings

Provides a general expression for N-string vertices

Utilizes matrix operations to represent string interactions

Unifies string interaction descriptions for arbitrary N

Abstract

We give the general form of the vertex corresponding to the interaction of an arbitrary number of strings. The technique employed relies on the ``comma" representation of String Field Theory where string fields and interactions are represented as matrices and operations between them such as multiplication and trace. The general formulation presented here shows that the interaction vertex of N strings, for any arbitrary N, is given as a function of particular combinations of matrices corresponding to the change of representation between the full string and the half string degrees of freedom.