Non-Rational 2D Quantum Gravity II. Target Space CFT

Abstract

We explore the formulation of non-rational 2D quantum gravity in terms of a chiral CFT on a Riemann surface associated with the target space. The CFT in question is constructed as the collective theory for a matrix chain, which is dual to a statistical height model on dynamical triangulations. The heights are associated with the sheets of the Riemann surface, which represents an infinite branched cover of the spectral plane. We consider two examples of height models: the SOS model and the semi-restricted SOS (SRSOS) model, in which the heights are restricted from below. Both models are described in the continuum limit by theories of 2D quantum gravity with conformal matter, perturbed by a thermal operator (1,3). We give a compact operator expression for the n-loop amplitudes as a collection of target space Feynman rules. The n-point functions of local fields are obtained by shrinking the loops. In particular, we show that the 4-point function of order operators in the SRSOS model coincides with the 4-point function of the ``diagonal'' world sheet CFT studied in [1].

48 pages, 11 figures, uses harvmac

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• Quantum Gravity from Timelike Liouville theory
• Infinitely many inequivalent field theories from one Lagrangian
• Matrix models as conformal field theories: genus expansion
• 2D quantum gravity partition function on the fluctuating sphere
• BRST cohomology of timelike Liouville theory
• Correlation Functions in Unitary Minimal Liouville Gravity and Frobenius Manifolds
• On non-homogeneous tachyon condensation in closed string theory
• The two-sphere partition function from timelike Liouville theory at three-loop order
• Boundary timelike Liouville theory: bulk 1-point & boundary 2-point functions