Hyperbolic Geometry and Closed Bosonic String Field Theory I: The String Vertices Via Hyperbolic Riemann Surfaces

Abstract

The main geometric ingredient of the closed string field theory are the string vertices, the collections of string diagrams describing the elementary closed string interactions, satisfying the quantum Batalian-Vilkovisky master equation. They can be characterized using the Riemann surfaces endowed with the metric solving the generalized minimal area problem. However, an adequately developed theory of such Riemann surfaces is not available yet, and consequently description of the string vertices via Riemann surfaces with the minimal area metric fails to provide practical tools for performing calculations. We describe an alternate construction of the string vertices satisfying the Batalian-Vilkovisky master equation using Riemann surfaces endowed with the metric having constant curvature $-1$ all over the surface. We argue that this construction provides an approximately gauge invariant closed string field theory.

46 pages, 16 figures, version to appear in JHEP

References in corpus (6)

• Closed Superstring Field Theory and its Applications
• Unitarity of Superstring Field Theory
• Unitarity of the Box Diagram
• Minimal-area metrics on the Swiss cross and punctured torus
• One Loop Tadpole in Heterotic String Field Theory
• Hyperbolic Geometry and Closed Bosonic String Field Theory II: The Rules for Evaluating the Quantum BV Master Action

Cited by in corpus (9)

• Closed Superstring Field Theory and its Applications
• String Field Theory as World-sheet UV Regulator
• D-instantons, String Field Theory and Two Dimensional String Theory
• Open-closed Hyperbolic String Vertices
• Open string stub as an auxiliary string field
• Hyperbolic Geometry and Closed Bosonic String Field Theory II: The Rules for Evaluating the Quantum BV Master Action
• Tree-level S-matrix of superstring field theory with homotopy algebra structure
• Quantum Closed Superstring Field Theory and Hyperbolic Geometry I: Construction of String Vertices
• Closed Bosonic String Tachyon Potential from the $\mathcal{N}=1$ Point of View