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 (33)

• Black Hole Attractors and the Topological String
• Exact Counting of Black Hole Microstates
• Corrections to macroscopic supersymmetric black-hole entropy
• Producing a Scale-Invariant Spectrum of Perturbations in a Hagedorn Phase of String Cosmology
• Ground Ring Of Two Dimensional String Theory
• c=1 String as the Topological Theory of the Conifold
• Macroscopic entropy formulae and non-holomorphic corrections for supersymmetric black holes
• Algebraic Structures and Differential Geometry in 2D String Theory
• Stringy corrections to Kahler potentials, SUSY breaking, and the cosmological constant problem
• Interaction of Discrete States in Two-Dimensional String Theory
• Hartle-Hawking Wave-Function for Flux Compactifications
• Topological String Partition Functions as Polynomials
• Exact S-Matrix for 2D String Theory
• Two Dimensional Yang-Mills, Black Holes and Topological Strings
• Baby Universes in String Theory
• The partition function of 2d string theory
• The Partition Function of the Two-Dimensional Black Hole Conformal Field Theory
• Time Lumps in Nonlocal Stringy Models and Cosmological Applications
• BPS Microstates and the Open Topological String Wave Function
• Peaks in the Hartle-Hawking Wave Function from Sums over Topologies
• N=8 Mechanics in SU(2)xSU(2) Harmonic Superspace
• Towards a Stringy Resolution of the Cosmological Singularity
• D-string fluid in conifold: I. Topological gauge model
• Wavefunction of the Universe on the Landscape
• Wave function of the Universe and Chern-Simons Perturbation Theory
• A Stringy Wave Function for an S^3 Cosmology
• Hyperkahler Singularities in Superstrings Compactification and 2d N=4 Conformal Field Theory
• Harmonic Superspaces from Superstrings
• HyperKhaler Metrics Building and Integrable Models
• Explicit Derivation of Yang-Mills Self-Dual Solutions on non-Commutative Harmonic Space
• Hartle-Hawking Vacuum for c=1 Tachyon Condensation
• Topological SL(2) Gauge Theory on Conifold
• On the harmonic superspace language adapted to the Gelfand-Dickey algebra of differential operators

Cited by in corpus (9)

• N=2 Supersymmetric Black Attractors in Six and Seven Dimensions
• Entropy of Pairs of Dual Attractors in 6D/7D
• On Black Hole Effective Potential in 6D/7D N=2 Supergravity
• Black Holes in Type IIA String on Calabi-Yau Threefolds with Affine ADE Geometries and q-Deformed 2d Quiver Gauge Theories
• Generalized MacMahon G(q) as q-deformed CFT Correlation Function
• Computing the Scalar Field Couplings in 6D Supergravity
• Topological String on Toric CY3s in Large Complex Structure Limit
• Geometry of the Ground State of Higgs Fields in Next-to-MSSM
• Generalized q-deformed Correlation Functions as Spectral Functions of Hyperbolic Geometry