Quantum Liouville Field Theory as Solution of a Flow Equation
arXiv:hep-th/9605039 · doi:10.1016/S0550-3213(97)00447-1
Abstract
A general framework for the Weyl invariant quantization of Liouville field theory by means of an exact renormalization group equation is proposed. This flow equation describes the scale dependence of the effective average action which has a built-in infrared cutoff. For c<1 it is solved approximately by a truncation of the space of action functionals. We derive the Ward identities associated to Weyl transformations in presence of the infrared cutoff. They are used to select a specific universality class for the renormalization group trajectory which is found to connect two conformal field theories with central charges 25-c and 26-c, respectively.
49 pages, latex
References in corpus (20)
- Exact evolution equation for the effective potential
- Critical Exponents from the Effective Average Action
- Derivative Expansion of the Exact Renormalization Group
- Flow Equations and BRS Invariance for Yang-Mills Theories
- On Truncations of the Exact Renormalization Group
- Kosterlitz-Thouless Phase Transition In The Two Dimensional Linear Sigma Model
- BRS symmetry for Yang-Mills theory with exact renormalization group
- The Renormalization Group and Two Dimensional Multicritical Effective Scalar Field Theory
- Ward identities and Wilson renormalization group for QED
- Fixed-Point Structure of Scalar Fields
- High Temperature Phase Transitions without Infrared Divergences
- Effective Average Action of Chern-Simons Field Theory
- Critical Exponents without the Epsilon Expansion
- Gradient Flows from an Approximation to the Exact Renormalization Group
- Radiatively-Induced First-Order Phase Transitions: The Necessity of the Renormalization Group
- Quantum and Thermal Fluctuations in Field Theory
- Coarse-Graining and Renormalization Group in the Einstein Universe
- On the Exact Operator Formalism of Two-Dimensional Liouville Quantum Gravity in Minkowski Spacetime
- The Many Faces of the Quantum Liouville Exponentials
- On gravitational dressing of renormalization group beta-functions beyond lowest order of perturbation theory
Cited by in corpus (32)
- Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
- Renormalization group improved black hole spacetimes
- Ultraviolet Fixed Point and Generalized Flow Equation of Quantum Gravity
- Flow Equation of Quantum Einstein Gravity in a Higher-Derivative Truncation
- Cosmology of the Planck Era from a Renormalization Group for Quantum Gravity
- Glass transition of a particle in a random potential, front selection in nonlinear RG and entropic phenomena in Liouville and SinhGordon models
- Is Quantum Einstein Gravity Nonperturbatively Renormalizable?
- Cosmology with Self-Adjusting Vacuum Energy Density from a Renormalization Group Fixed Point
- Bimetric Truncations for Quantum Einstein Gravity and Asymptotic Safety
- Background Independence and Asymptotic Safety in Conformally Reduced Gravity
- A class of nonlocal truncations in Quantum Einstein Gravity and its renormalization group behavior
- Renormalization-group running cosmologies - a scale-setting procedure
- Confronting the IR Fixed Point Cosmology with High Redshift Observations
- Cosmological Perturbations in Renormalization Group Derived Cosmologies
- The Renormalization Group and Weyl-invariance
- Bare Action and Regularized Functional Integral of Asymptotically Safe Quantum Gravity
- Conformally reduced quantum gravity revisited
- The role of Background Independence for Asymptotic Safety in Quantum Einstein Gravity
- Gravity with more or less gauging
- A link that matters: Towards phenomenological tests of unimodular asymptotic safety
- Composite Operators in Asymptotic Safety
- The unitary conformal field theory behind 2D Asymptotic Safety
- Rotation Symmetry Breaking Condensate in a Scalar Theory
- Towards a -function in 4D quantum gravity
- An algebraic QFT approach to the Wetterich equation on Lorentzian manifolds
- Geometric operators in the asymptotic safety scenario for quantum gravity
- A Shape Dynamical Approach to Holographic Renormalization
- Flow equation for Halpern-Huang directions of scalar O(N) models
- Non-perturbative scaling in the scalar theory
- Random Energy Model with complex replica number, complex temperatures and classification of the string's phases
- Non-renormalization for the Liouville wave function
- Gravitational action for a massive Majorana fermion in 2d quantum gravity