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.

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 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 Near conformal perturbation theory in SYK type models

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Sumit R. Das ◽  
Animik Ghosh ◽  
Antal Jevicki ◽  
Kenta Suzuki
Keyword(s):  
Perturbation Theory ◽  
Correlation Function ◽  
Effective Action ◽  
Correlation Functions ◽  
Conformal Invariance ◽  
Soft Mode ◽  
Energy Scale ◽  
Low Energy ◽  
Liouville Theory ◽  
Breaking Term

Abstract We present a systematic procedure to extract the dynamics of the low energy soft mode in SYK type models with a single energy scale J and emergent reparametrization symmetry in the IR. This is given in the framework of the perturbative scheme of arXiv:1608.07567 based on a specific (off-shell) breaking of conformal invariance in the UV, adjusted to yield the exact large-N saddle point. While this breaking term formally vanishes on-shell, it has a non-trivial effect on correlation functions and the effective action. In particular, it leads to the Schwarzian action with a specific coupling to bi-local matter. The method is applied to the evaluation of O(1) corrections to the correlation function of bi-locals. As a byproduct we confirm precise agreement with the explicit, symmetry breaking procedure. We provide a verification in the large q limit (Liouville theory), where the correlators can be calculated exactly at all length scales. In this case, our scheme illuminates how the enhanced O(J) and the subleading O(1) contributions originate from the Schwarzian dynamics of the soft mode and its interaction with h = 2 (bi-local) matter.

scholarly journals EFFECTIVE THEORY FOR QUANTUM GRAVITY

2013 ◽  
Vol 22 (12) ◽  
pp. 1342014 ◽  
Author(s):  
XAVIER CALMET
Keyword(s):  
Higgs Boson ◽  
Quantum Gravity ◽  
Effective Action ◽  
Binary Systems ◽  
Ricci Scalar ◽  
Effective Theory ◽  
Nonminimal Coupling ◽  
Order Unity

In this paper, we discuss an effective theory for quantum gravity and discuss the bounds on the parameters of this effective action. In particular, we show that measurement in pulsars binary systems are unlikely to improve the bounds on the coefficients of the R2 and RμνRμν terms obtained from probes of Newton's potential performed on Earth. Furthermore, we argue that if the coefficients of these terms are induced by quantum gravity, they should be at most of order unity since R2 and RμνRμν are dimension four operators. The same applies to the nonminimal coupling of the Higgs boson to the Ricci scalar.

THE VILKOVISKY EFFECTIVE ACTION IN THE EVEN-DIMENSIONAL QUANTUM GRAVITY

1989 ◽  
Vol 04 (07) ◽  
pp. 633-644 ◽  
Author(s):  
I. L. BUCHBINDER ◽  
E. N. KIRILLOVA ◽  
S. D. ODINTSOV
Keyword(s):  
Numerical Calculation ◽  
Effective Potential ◽  
Effective Action ◽  
Equations Of Motion ◽  
Flat Space ◽  
Einstein Gravity ◽  
Quantum Field ◽  
Dimensional Torus ◽  
Spontaneous Compactification ◽  
The One

The one-loop Vilkovisky effective potential which is not dependent on a gauge and a parametrization of quantum field, is investigated. We have considered Einstein gravity on a background manifold of (flat space) × (d−4- sphere) or × (d−4- dimensional torus ), d is even, and of R3 × (1- sphere ), where R3 is flat space. The numerical calculation for the cases R4 × Td−4 (d = 6,8,10) and R3 × S1 is done. The solution to the one-loop corrected equations of motion is found, although the spontaneous compactification is not stable in these cases.

THE FERMION-FERMION EFFECTIVE ACTION FOR THE THREE-DIMENSIONAL MASSIVE THIRRING MODEL

1994 ◽  
Vol 09 (18) ◽  
pp. 3143-3151 ◽  
Author(s):  
R.F. RIBEIRO ◽  
E.R. BEZERRA DE MELLO
Keyword(s):  
Schrödinger Equation ◽  
Effective Potential ◽  
Effective Action ◽  
Schrodinger Equation ◽  
Three Dimensional ◽  
Bound State ◽  
Thirring Model ◽  
Coupling Constant ◽  
Massive Thirring Model

In this paper a nonrelativistic fermion-fermion effective potential for a three-dimensional massive Thirring model is obtained in a 1/N expansion. We show, by analyzing the Schrödinger equation in the presence of this potential, that the system presents a fermion-fermion bound state for a positive value of the coupling constant g.

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