Bootstrapping closed string field theory

• Published in: arXiv.org
• Main Author: Atakan Hilmi Fırat
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 14.06.2023
• Subjects: Apexes; Field theory; Liouville equations; Mathematics - Complex Variables; Momentum; Physics - High Energy Physics - Theory; Strings; Tachyons
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2302.12843

The determination of the string vertices of closed string field theory is shown to be a conformal field theory problem solvable by combining insights from Liouville theory, hyperbolic geometry, and conformal bootstrap. We first demonstrate how Strebel differentials arise from hyperbolic string vertices by performing a WKB approximation to the associated Fuchsian equation, which we subsequently use it to derive a Polyakov-like conjecture for Strebel differentials. This result implies that the string vertices are generated by the interactions of \(n\) zero momentum tachyons, or equivalently, a certain limit of suitably regularized on-shell Liouville action. We argue that the latter can be related to the interaction of three zero momentum tachyons on a generalized cubic vertex through classical conformal blocks. We test this claim for the quartic vertex and discuss its generalization to higher-string interactions.