Bootstrapping closed string field theory
Abstract
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.
- Publication:
-
Journal of High Energy Physics
- Pub Date:
- May 2023
- DOI:
- 10.1007/JHEP05(2023)186
- arXiv:
- arXiv:2302.12843
- Bibcode:
- 2023JHEP...05..186F
- Keywords:
-
- String Field Theory;
- Differential and Algebraic Geometry;
- High Energy Physics - Theory;
- Mathematics - Complex Variables
- E-Print:
- 42+15 pages, 8 figures