Logarithmic conformal field theory and Seiberg-Witten models

Abstract

The periods of arbitrary abelian forms on hyperelliptic Riemann surfaces, in particular the periods of the meromorphic Seiberg-Witten differential λ SW, are shown to be in one-to-one correspondence with the conformal blocks of correlation functions of the rational logarithmic conformal field theory with central charge c= c 2,1=−2. The fields of this theory precisely simulate the branched double covering picture of a hyperelliptic curve, such that generic periods can be expressed in terms of certain generalised hypergeometric functions, namely the Lauricella functions of type F D .