Virasoro correlation functions on hyperelliptic Riemann surfaces
Marianne Leitner (Dublin Institute for Advanced Studies)
Tuesday 22nd January, 2013 15:00-16:00 Maths 416
$N$-point functions of holomorphic fields in conformal field theories can be calculated by methods from algebraic geometry. 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. All correlation functions involve a finite number of parameters whose determination in general requires different tools. For the $(2,5)$-minimal model, we fully determine the Virasoro $2$-point function for $g=1$ and both the $2$-and the $3$-point function for $g=2$.