Remarks on Free Field Realization on SL(2,R)/U(1) \times U(1) WZNW Model

GASTÓN E. GIRIBET, DANIEL E. LOPEZ -FOGLIANI

JOURNAL OF HIGH ENERGY PHYSICS - (Online)

IOP & SISSA

Año: 2004 vol. 0406 p. 26 - 54

1029-8479

Free field representations of vertex algebra in $SL(2, R)_k /U(1) × U(1)$ WZNW model are constructed by considering a twisted version of the Bershadsky-Kutasov free field description of discrete states in the two-dimensional black hole CFT. These correspond to conjugate representations describing primary states in the model on $SL(2, R)/U(1) × U(1)$. A particular evaluation of these leads to identities due to the spectral flow symmetry of $sl(2)_k$ algebra. The computation of correlation functions violating the ωinding number conservation is discussed and, as an application, these are compared with analogous results known for the sine-Liouville theory. Exact agreement is observed between both analytic structures.