Topological string in harmonic space and correlation functions in $S^3$ stringy cosmology

Abstract

We develop the harmonic space method for conifold and use it to study local complex deformations of $T^{\ast }{S}^3$ preserving manifestly $SL(2,C)$ isometry. We derive the perturbative manifestly $SL(2,C)$ invariant partition function ${\mathcal{Z}}_{top}$ of topological string B model on locally deformed conifold. Generic $n$ momentum and winding modes of 2D $c=1$ non critical theory are described by highest and lowest components ${\upsilon }_{(0,n)}$ of $SL(2,C)$ spin $s=\frac{n}{2}$ multiplets , $0\le k\le n$ 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 $U_{\alpha }^{+}$ and $V_{\alpha }^{-}$. We also derive a dictionary giving the passage from Laurent (Fourier) analysis on $T^{\ast }{S}^1$ ($S^1$) to the harmonic method on $T^{\ast }{S}^3$ ($S^3$). The manifestly $SU(2,C)$ covariant correlation functions of the $S^3$ quantum cosmology model of Gukov-Saraikin-Vafa are also studied.

91 pages

References in corpus (4)

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• BPS Microstates and the Open Topological String Wave Function
• Towards a Stringy Resolution of the Cosmological Singularity
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