Quantum Closed Superstring Field Theory and Hyperbolic Geometry I: Construction of String Vertices

TL;DR

This paper develops a quantum closed superstring field theory framework using hyperbolic geometry, constructing string vertices with specific geometric and analytic properties to satisfy the quantum master equation.

Contribution

It introduces a novel construction of string vertices on hyperbolic surfaces with analytic local coordinates and picture changing operators, satisfying the quantum BV master equation.

Findings

Constructed string vertices with constant negative curvature metric.

Ensured compatibility with the quantum BV master equation.

Integrated hyperbolic geometry into superstring field theory.

Abstract

The complete quantum theory of closed superstrings is constructed using string diagrams endowed with metric having constant curvature $-1$. The elementary string diagrams are equipped with the analytic local coordinates induced from the hyperbolic metric and a distribution of a set of picture changing operators constructed using the identities satisfied by the simple closed geodesics on a hyperbolic Riemann surface. However, a slight modification near the boundary of the string vertices is needed to make them satisfy the geometric condition imposed by the quantum Batalin-Vilkovisky master equation.