On string fields and superstring field theories

TL;DR

This paper explores the structure of string fields, focusing on mid-point insertions and their implications for superstring field theories, proposing regularization and extensions to address issues with non-zero conformal weight insertions.

Contribution

It introduces a new perspective on the space of string fields as an odd component of a star-algebra and discusses regularization methods for mid-point insertions in superstring field theories.

Findings

Mid-point insertions can be well-behaved despite having a non-trivial kernel.

The non-minimal superstring field theory can support known solutions, including the GSO+ vacuum.

Regularization or extension of the non-minimal sector can address issues with conformal weight insertions.

Abstract

We offer some thoughts regarding the space of string fields. We suggest that this space should be identified as the odd component of a star-algebra and focus among other issues on the role of the mid-point. We argue that theories with mid-point insertions in the action, such as the modified cubic theory can be well behaved, even if this mid-point insertion has a non-trivial kernel. We then discuss the recent proposal by Berkovits and Siegel of a non-minimal superstring field theory. In this theory the action contains a mid-point insertion of a non-zero conformal weight. We show that, while this is a-priori a problem, it might be possible (in the NS sector) to make sense out of this theory by regularizing it. A cleaner resolution of the problem is to extend the non-minimal sector in a way that allows a zero-weight mid-point insertion with the desired properties. We also study the generalisation of the theory to the NS- sector and explain the problems with defining the Ramond sectors. We show that the non-minimal theory supports all the known solutions of the standard modified cubic superstring field theory, including the GSO+ vacuum solution. The properties of the solutions carry over to the non-minimal theory. In particular, the vacuum solution has the correct tension and cohomology.