Topological recursion for hyperbolic string field theory

Abstract

We derive an analog of Mirzakhani's recursion relation for hyperbolic string vertices and investigate its implications for closed string field theory. Central to our construction are systolic volumes: the Weil-Petersson volumes of regions in moduli spaces of Riemann surfaces whose elements have systoles $L\ge 0$. These volumes can be shown to satisfy a recursion relation through a modification of Mirzakhani's recursion as long as $L\le 2{\sinh }^{-1}1$. Applying the pants decomposition of Riemann surfaces to off-shell string amplitudes, we promote this recursion to hyperbolic string field theory and demonstrate the higher order vertices are determined by the cubic vertex iteratively for any background. Such structure implies the solutions of closed string field theory obey a quadratic integral equation. We illustrate the utility of our approach in an example of a stubbed scalar theory.

arXiv comment46+10 pages, 12 figures, 2 tables

References in corpus (48)

• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Introduction to string field theory
• Closed String Field Theory: Quantum Action and the BV Master Equation
• Descent Relations Among Bosonic D-branes
• Instantons and recursion relations in N=2 Susy gauge theory
• Universality of the Tachyon Potential
• Geometry of Batalin-Vilkovisky quantization
• Proof of vanishing cohomology at the tachyon vacuum
• Recursive representation of the torus 1-point conformal block
• Closed Superstring Field Theory and its Applications
• Quantum Background Independence of Closed String Field Theory
• A Closed String Tachyon Vacuum ?
• Off-shell Amplitudes in Superstring Theory
• Developing the Covariant Batalin-Vilkovisky approach to String Theory
• The Dilaton Theorem and Closed String Backgrounds
• Four Lectures on Closed String Field Theory
• String Field Theory -- A Modern Introduction
• Classical geometry from the quantum Liouville theory
• Uniformization theory and 2D gravity I. Liouville action and intersection numbers
• Classical torus conformal block, N=2* twisted superpotential and the accessory parameter of Lame equation
• Off-shell Closed String Amplitudes: Towards a Computation of the Tachyon Potential
• Hyperbolic three-string vertex
• Open-closed Hyperbolic String Vertices
• The closed string field theory action vanishes
• The ABCD of topological recursion
• Liouville theory and uniformization of four-punctured sphere
• Effective Tachyonic Potential in Closed String Field Theory
• Closed Bosonic String Field Theory At Quartic Order
• Closed Bosonic String Field Theory at Quintic Order: Five-Tachyon Contact Term and Dilaton Theorem
• Closed Bosonic String Field Theory at Quintic Order II: Marginal Deformations and Effective Potential
• Classical Liouville action on the sphere with three hyperbolic singularities
• Bootstrapping closed string field theory
• Open string field theory with stubs
• Polyakov conjecture for hyperbolic singularities
• Hyperbolic string tadpole
• Open string stub as an auxiliary string field
• QFT with Stubs
• Closed string theory without level-matching at the free level
• The nonperturbative closed string tachyon vacuum to high level
• The Liouville Geometry of N=2 Instantons and the Moduli of Punctured Spheres
• Vacuum vertices and the ghost-dilaton
• String Field Theory
• Connections between reflected entropies and hyperbolic string vertices
• Nonperturbative Model Of Liouville Gravity
• Wilsonian effective potentials and closed string field theory
• String vertices for the large $N$ limit
• Characterizing 4-string contact interaction using machine learning
• Topological conformal field theories and gauge theories

Cited by in corpus (4)

• The complex Liouville string: the matrix integral
• Boundary terms in string field theory
• Symplectic structure in open string field theory I: Rolling tachyons
• Symplectic structure in open string field theory III: Electric field