Exactly Marginal Operators and Running Coupling Constants in 2D Gravity

Abstract

The Liouville action for two--dimensional quantum gravity coupled to interacting matter contains terms that have not been considered previously. They are crucial for understanding the renormalization group flow and can be observed in recent matrix model results for the phase diagram of the Sine--Gordon model coupled to gravity. These terms insure, order by order in the coupling constant, that the dressed interaction is exactly marginal. They are discussed up to second order.

22 pages, plain Tex, CALT-68-1817 (Some modifications but same results. Figures will be faxed upon request.)

References in corpus (3)

• Interaction of Discrete States in Two-Dimensional String Theory
• Irreversibility of the Renormalization Group Flow in Two Dimensional Quantum Gravity
• Path Integral Over Conformally Self-Dual Geometries

Cited by in corpus (24)

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• Indecomposable Fusion Products
• An Introduction to Conformal Field Theory
• A Microscopic Liouville Arrow of Time
• On string cosmology and the RG flow in 2d field theory
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• Logarithmic Operators in Conformal Field Theory and The $\W_\infty$-algebra
• Physical Scaling and Renormalization Group in Two-Dimensional Gravity
• Time-Dependent Backgrounds in 2D String Theory and the $S$-matrix Generating Functional
• FZZ Algebra
• On gravitational dressing of renormalization group beta-functions beyond lowest order of perturbation theory
• RG flow on random surfaces with handles and closed string field theory
• Gravitationally dresed RG flows and zig-zag invariant strings
• Supergravity dressing of beta-functions in N=1 and N=2 supersymmetric models
• Renormalization Group Flows in Sigma--Models Coupled to Two--Dimensional Dynamical Gravity
• Gravitational action for a massive Majorana fermion in 2d quantum gravity
• On scheme dependence of gravitational dressing of renormalization group functions
• Field condensations and Noncritical String for c>1
• Gravitational dressing of massive soliton theories
• Towards c=0 Flows
• Wrapped M-branes and Three-dimensional Topologies
• Solitonic d-5 brane and Vortex on the World-Sheet
• CP^{N-1} models and the Quantized 2D Black Holes
• Gravitational Dressing of N=2 Sigma-Models Beyond Leading Order