Open-closed Hyperbolic String Vertices

TL;DR

This paper develops a new family of hyperbolic string vertices for open-closed string field theory, extending previous work on closed strings by using hyperbolic surfaces and collar theorems to define and describe these vertices.

Contribution

It introduces a generalized construction of hyperbolic string vertices for open-closed theories, including explicit descriptions for low-dimensional moduli spaces.

Findings

Construction of hyperbolic string vertices using bordered hyperbolic surfaces

Application of collar theorems to restrict systolic conditions

Explicit descriptions for zero and one-dimensional moduli spaces

Abstract

We construct a family of hyperbolic string vertices in the oriented open-closed string field theory, generalizing the recent result on hyperbolic closed string vertices by Costello and Zwiebach. The vertices are described by certain bordered hyperbolic surfaces and we explain relevant collar theorems which provide restrictions on the systolic conditions for the hyperbolic vertices. We also give explicit descriptions of the vertices for all zero and one-dimensional moduli spaces.