Abstract
We develop the harmonic space method for conifold and use it to study local complex deformations of T * S 3 preserving manifestly SL ( 2 , C ) isometry. We derive the perturbative manifestly SL ( 2 , C ) invariant partition function Z top 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 = n 2 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 U α + and V α − . We also derive a dictionary giving the passage from Laurent (Fourier) analysis on T * S 1 ( S 1 ) to the harmonic method on T * S 3 ( S 3 ). The manifestly SU ( 2 , C ) covariant correlation functions of the S 3 quantum cosmology model of Gukov–Saraikin–Vafa are also studied.
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