1. Topological recursion for hyperbolic string field theory
- Author
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Fırat, Atakan Hilmi and Valdes-Meller, Nico
- Subjects
Particle and High Energy Physics ,Mathematical Physics ,Pure Mathematics ,Mathematical Sciences ,Physical Sciences ,String Field Theory ,Bosonic Strings ,Tachyon Condensation ,Matrix Models ,Atomic ,Molecular ,Nuclear ,Particle and Plasma Physics ,Quantum Physics ,Nuclear & Particles Physics ,Mathematical physics ,Nuclear and plasma physics ,Particle and high energy physics - 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 ≥ 0. These volumes can be shown to satisfy a recursion relation through a modification of Mirzakhani’s recursion as long as L ≤ 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.
- Published
- 2024