Hyperbolic string tadpole

Hyperbolic geometry on the one-bordered torus is numerically uniformized using Liouville theory. This geometry is relevant for the hyperbolic string tadpole vertex describing the one-loop quantum corrections of closed string field theory. We argue that the Lamé equation, upon fixing its accessory pa...

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Bibliographic Details
Published inarXiv.org
Main Author Atakan Hilmi Fırat
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 13.12.2023
Subjects
Field theory
Lame functions
Liouville equations
Mathematics - Complex Variables
Physics - High Energy Physics - Theory
String theory
Toruses
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Summary:Hyperbolic geometry on the one-bordered torus is numerically uniformized using Liouville theory. This geometry is relevant for the hyperbolic string tadpole vertex describing the one-loop quantum corrections of closed string field theory. We argue that the Lamé equation, upon fixing its accessory parameter via Polyakov conjecture, provides the input for the characterization. The explicit expressions for the Weil-Petersson metric as well as the local coordinates and the associated vertex region for the tadpole vertex are given in terms of classical torus conformal blocks. The relevance of this vertex for vacuum shift computations in string theory is highlighted.
Bibliography:MIT-CTP/5568
ISSN:2331-8422
DOI:10.48550/arxiv.2306.08599