# Virasoro correlation functions on hyperelliptic Riemann surfaces

### Marianne Leitner (Dublin Institute for Advanced Studies)

Tuesday 22nd January, 2013 15:00-16:00 Maths 416

#### Abstract

\$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\$.