On surface states and star-subalgebras in string field theory

TL;DR

This paper explores the relationship between surface states and squeezed states in string field theory, providing criteria for their equivalence, classifying states within specific subalgebras, and introducing generalized mappings for surface state classification.

Contribution

It establishes equivalent criteria for surface and squeezed states, classifies surface states in a key subalgebra, and introduces a generalized Schwarz-Christoffel mapping for surface state analysis.

Findings

Surface and squeezed states criteria are equivalent.

The H_{κ^2} subalgebra contains only wedge states and butterflies.

A new family of surface state subalgebras is described using generalized Schwarz-Christoffel mappings.

Abstract

We elaborate on the relations between surface states and squeezed states. First, we investigate two different criteria for determining whether a matter sector squeezed state is also a surface state and show that the two criteria are equivalent. Then, we derive similar criteria for the ghost sector. Next, we refine the criterion for determining whether a surface state is in H_{\kappa^2}, the subalgebra of squeezed states obeying [S,K_1^2]=0. This enables us to find all the surface states of the H_{\kappa^2} subalgebra, and show that it consists only of wedge states and (hybrid) butterflies. Finally, we investigate generalizations of this criterion and find an infinite family of surface states subalgebras, whose surfaces are described using a "generalized Schwarz-Christoffel" mapping.