Rational CFTs on Riemann surfaces
Marianne Leitner, Werner Nahm
TL;DR
This paper explores the behavior of rational conformal field theories on Riemann surfaces, deriving specific differential equations for hyperelliptic surfaces within the context of the $(2,5)$ minimal model.
Contribution
It provides the first derivation of Gauss-Manin type ODEs for rational CFTs on hyperelliptic Riemann surfaces, specifically for the $(2,5)$ minimal model.
Findings
Derived the ODE system for the $(2,5)$ minimal model on hyperelliptic surfaces
Confirmed the expected Gauss-Manin type differential equations for these CFTs
Enhanced understanding of CFT partition functions on complex Riemann surfaces
Abstract
The partition function of rational conformal field theories (CFTs) on Riemann surfaces is expected to satisfy ODEs of Gauss-Manin type. We investigate the case of hyperelliptic surfaces and derive the ODE system for the minimal model.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Black Holes and Theoretical Physics · Advanced Algebra and Geometry