Extended multiplet structure in Logarithmic Conformal Field Theories

We use the process of quantum hamiltonian reduction of SU(2)k, at rational level k, to study explicitly the correlators of the h1,s fields in the cp,q models. We find from direct calculation of the correlators that we have the possibility of extra, chiral and non-chiral, multiplet structure in the h1,s operators beyond the ‘minimal’ sector. At the level of the vacuum null vector h1,2p−1 = (p − 1)(q − 1) we find that there can be two extra non-chiral fermionic fields. The extra indicial structure present here permeates throughout the entire theory. In particular we find we have a chiral triplet of fields at h1,4p−1 = (2p−1)(2q −1). We conjecture that this triplet algebra may produce a rational extended cp,q model. We also find a doublet of fields at h1,3p−1 = ( 3p 2 − 1)( 3q 2 − 1). These are chiral fermionic operators if p and q are not both odd and otherwise parafermionic. [email protected]