Topological string in harmonic space and correlation functions in S3 stringy cosmology

We develop the harmonic space method for conifold and use it to study local complex deformations of T*S3 preserving manifestly SL(2,C) isometry. We derive the perturbative manifestly SL(2,C) invariant partition function Ztop of topological string B model on locally deformed conifold. Generic n momentum and winding modes of 2D c=1 noncritical theory are described by highest υ(n,0) and lowest components υ(0,n) of SL(2,C) spin s=n2 multiplets (υ(n−k,k)), 0⩽k⩽n and are shown to be naturally captured by harmonic monomials. Isodoublets (n=1) describe uncoupled units of momentum and winding modes and are exactly realized as the SL(2,C) harmonic variables Uα+ and Vα−. We also derive a dictionary giving the passage from Laurent (Fourier) analysis on T*S1 (S1) to the harmonic method on T*S3 (S3). The manifestly SU(2,C) covariant correlation functions of the S3 quantum cosmology model of Gukov-Saraikin-Vafa are also studied.