Notes on Quantum Liouville Theory and Quantum Gravity

1991 ◽  
pp. 363-395 ◽  
Author(s):  
Nathan Seiberg
Keyword(s):  
Quantum Gravity ◽  
Liouville Theory

scholarly journals Quantum gravity from timelike Liouville theory

2019 ◽  
Vol 2019 (10) ◽  
Author(s):  
Teresa Bautista ◽  
Atish Dabholkar ◽  
Harold Erbin
Keyword(s):  
Quantum Gravity ◽  
Liouville Theory

2-D QUANTUM GRAVITY AND LIOUVILLE THEORY

1990 ◽  
Vol 05 (18) ◽  
pp. 1411-1421 ◽  
Author(s):  
ERIC D’HOKER ◽  
P.S. KURZEPA
Keyword(s):  
Invariant Measure ◽  
Quantum Gravity ◽  
First Principles ◽  
Liouville Theory ◽  
Translation Invariant ◽  
Anomalous Dimensions ◽  
Conformal Gauge ◽  
Liouville Action

We quantize the Liouville theory, or 2-D quantum gravity, and quantum supergravity in the conformal gauge. We explicitly calculate the Jacobian accompanying the change from the Weyl invariant measure to the translation invariant one. We show that it is of the same form as the original Liouville action, thus establishing a conjecture of David and Distler and Kawai. This calculation yields dressed gravitational central charges and anomalous dimensions from first principles.

scholarly journals Boundary Liouville theory and 2D quantum gravity

2004 ◽  
Vol 683 (3) ◽  
pp. 309-362 ◽  
Author(s):  
Ivan K. Kostov ◽  
Bénédicte Ponsot ◽  
Didina Serban
Keyword(s):  
Quantum Gravity ◽  
Liouville Theory

scholarly journals RENORMALIZATION GROUP EFFECTS IN THE CONFORMAL SECTOR OF 4D QUANTUM GRAVITY WITH MATTER

1994 ◽  
Vol 09 (22) ◽  
pp. 2041-2047 ◽  
Author(s):  
S. ODINTSOV ◽  
R. PERCACCI
Keyword(s):  
Renormalization Group ◽  
Gauge Theory ◽  
Quantum Gravity ◽  
Effective Potential ◽  
Gauge Coupling ◽  
Liouville Theory ◽  
Gross Neveu Model ◽  
Group Effects

We discuss the “gravitationally dressed” beta functions in the Gross-Neveu model interacting with 2d Liouville theory and in SU(N) gauge theory interacting with the conformal sector of 4d quantum gravity. Among the effects we suggest one may feel that the gravitational dressing are the minimum of the effective potential and the running of the gauge coupling.

scholarly journals The two-sphere partition function in two-dimensional quantum gravity

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Dionysios Anninos ◽  
Teresa Bautista ◽  
Beatrix Mühlmann
Keyword(s):  
Partition Function ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Path Integral ◽  
Central Charge ◽  
Liouville Theory ◽  
Two Dimensional ◽  
Positive Cosmological Constant ◽  
Gauge Fixing ◽  
Semiclassical Expansion

Abstract We study the Euclidean path integral of two-dimensional quantum gravity with positive cosmological constant coupled to conformal matter with large and positive central charge. The problem is considered in a semiclassical expansion about a round two-sphere saddle. We work in the Weyl gauge whereby the computation reduces to that for a (timelike) Liouville theory. We present results up to two-loops, including a discussion of contributions stemming from the gauge fixing procedure. We exhibit cancelations of ultraviolet divergences and provide a path integral computation of the central charge for timelike Liouville theory. Combining our analysis with insights from the DOZZ formula we are led to a proposal for an all orders result for the two-dimensional gravitational partition function on the two-sphere.

EQUIVALENCE OF LIOUVILLE THEORY AND 2-D QUANTUM GRAVITY

1991 ◽  
Vol 06 (09) ◽  
pp. 745-767 ◽  
Author(s):  
ERIC D’HOKER
Keyword(s):  
Perturbation Theory ◽  
Invariant Measure ◽  
Quantum Gravity ◽  
Effective Potential ◽  
Effective Action ◽  
Liouville Theory ◽  
Ward Identities ◽  
Explicit Equation ◽  
Translation Invariant

The equivalence of 2-dimensional quantum gravity and Liouville theory quantized with the standard translation invariant measure, is shown to hold to all orders in perturbation theory. Also, an explicit equation for the Liouville effective action as a function of the effective potential is derived from Weyl Ward identities. We speculate on some of the non-perturbative aspects of the theory.

Sign in / Sign up

Export Citation Format

Share Document