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.

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.

Two-dimensional quantum gravity in the conformal gauge

1990 ◽  
Vol 42 (4) ◽  
pp. 1144-1146 ◽  
Author(s):  
Chang Jun Ahn ◽  
Young Jai Park ◽  
Kee Yong Kim ◽  
Yongduk Kim ◽  
Won Tae Kim ◽  
...  
Keyword(s):  
Quantum Gravity ◽  
Two Dimensional ◽  
Conformal Gauge

scholarly journals Conformal gauge generators in Liouville theory

1994 ◽  
Vol 11 (9) ◽  
pp. 2143-2153
Author(s):  
M Blagojevic ◽  
M Vasilic ◽  
T Vukasinac
Keyword(s):  
Liouville Theory ◽  
Conformal Gauge

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

scholarly journals EXACT SOLUTIONS TO THE TWO-DIMENSIONAL BF AND YANG–MILLS THEORIES IN THE LIGHT-CONE GAUGE

2002 ◽  
Vol 17 (11) ◽  
pp. 1491-1502 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Exact Solution ◽  
Quantum Gravity ◽  
Light Cone ◽  
Lagrangian Density ◽  
Critical Dimension ◽  
Two Dimensional ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Bf Theory ◽  
Conformal Gauge

It is shown that the BRS (= Becchi–Rouet–Stora)-formulated two-dimensional BF theory in the light-cone gauge (coupled with chiral Dirac fields) is solved very easily in the Heisenberg picture. The structure of the exact solution is very similar to that of the BRS-formulated two-dimensional quantum gravity in the conformal gauge. In particular, the BRS Noether charge has anomaly. Based on this fact, a criticism is made on the reasoning of Kato and Ogawa, who derived the critical dimension D=26 of string theory on the basis of the anomaly of the BRS Noether charge. By adding the [Formula: see text] term to the BF-theory Lagrangian density, the exact solution to the two-dimensional Yang–Mills theory is also obtained.

ON THE ALGEBRAIC STRUCTURE of QUANTUM GRAVITY IN TWO DIMENSIONS

1991 ◽  
Vol 06 (16) ◽  
pp. 2805-2827 ◽  
Author(s):  
Jean-Loup Gervais
Keyword(s):  
Quantum Gravity ◽  
Quantum Group ◽  
Algebraic Structure ◽  
Group Structure ◽  
Two Dimensions ◽  
Conformal Gauge

Current progresses in understanding quantum gravity from the operator viewpoint are reviewed. They are based on the Uq(sl(2))-quantum-group structure recently put forward1,2, for the chiral components of the metric in the conformal gauge.

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