Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-04-27
Nucl.Phys.B748:380-457,2006
Physics
High Energy Physics
High Energy Physics - Theory
91 pages
Scientific paper
10.1016/j.nuclphysb.2006.04.020
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 $% \upsilon_{(n,0)}$ and lowest components $\upsilon_{(0,n)}$ of $SL(2,C) $ spin $s=\frac{n}{2}$ multiplets $% (\upsilon _{(n-k,k)}) $, $0\leq k\leq n$ 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.
Saidi El Hassan
Sedra Moulay Brahim
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