CFT 2011

We introduce the intertwined partition and $n$-point correlation functions for a vertex operator superalgebra on a genus two Riemann surface formed by self-sewing of the torus. In fundamental example of the free fermion vertex operator superalgebra we prove that the intertwined partition function is holomorphic in the sewing parameter. Using the explicit representation for vertex operators of a generalized vertex algebra for Heisenberg intetwiners [TZ2] we obtain a closed formula for the genus two intertwined partition function as an infinite dimensional determinant with entries arising from Szeg\H{o} kernel on original torus [TZ1]. We then compute the generating function for all genus two $n$-point twisted correlation functions in terms of the genus two Szeg\H{o} kernel determinant and discuss their modular properties. A genus two generalization for Jacobi triple product identity will be discussed [TZ1].

Donnerstag, den 22. September 2011 um 14:30 Uhr, in INF288, HS1 Donnerstag, den 22. September 2011 at 14:30, in INF288, HS1