Universal regularization for string field theory

TL;DR

This paper introduces a universal, analytical regularization method for string field theory calculations that simplifies geometric interpretation and improves the consistency of inner product evaluations and algebraic relations.

Contribution

The authors develop a new analytical regularization technique with a geometric basis, applicable to various bases and calculations in string field theory, enhancing consistency and simplicity.

Findings

Inner products of wedge states equal unity with the new regularization

Unwanted constants in Schnabl's algebra vanish using this regularization

Regularization is applicable to both discrete and continuous bases

Abstract

We find an analytical regularization for string field theory calculations. This regularization has a simple geometric meaning on the worldsheet, and is therefore universal as level truncation. However, our regularization has the added advantage of being analytical. We illustrate how to apply our regularization to both the discrete and continuous basis for the scalar field and for the bosonized ghost field, both for numerical and analytical calculations. We reexamine the inner products of wedge states, which are known to differ from unity in the oscillator representation in contrast to the expectation from level truncation. These inner products describe also the descent relations of string vertices. The results of applying our regularization strongly suggest that these inner products indeed equal unity. We also revisit Schnabl's algebra and show that the unwanted constant vanishes when using our regularization even in the oscillator representation.