CFTs on Riemann Surfaces of genus $g\geq 1$

Details CFTs on Riemann Surfaces of genus $g\geq 1$ CFTs on Riemann Surfaces of genus $g\geq 1$

2010-11-07

arxiv.org/abs/1011.1632v3

Mathematics

Complex Variables

Graph representation worked out; this yields the formula for the Virasoro $N$-point function for arbitrary $N$. (29 pages)

Scientific paper

$N$-point functions of holomorphic fields in rational conformal field theories can be calculated by methods from complex analysis. We establish explicit formulas for the 2-point function of the Virasoro field on hyperelliptic Riemann surfaces of genus $g\geq 1$. $N$-point functions for higher $N$ are obtained inductively, and we show that they have a nice graph representation. We discuss the 3-point function with application to the $(2,5)$ minimal model.

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