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Conformal field theoretical approach to two-dimensional quantum gravity

Technical Report:

Abstract

A conformal (or Weyl) mode of two-dimensional gravity coupled to conformally invariant matter, which is a gauge degree of freedom in the classical level, becomes dynamical through the conformal (or Weyl) anomaly. We consider the BRS quantization of the above system in the conformal gauge. As a practical approach which enables us to do explicit calculations, we reduce the BRS invariant path integral measure for the conformal mode to the naive one by including a one-loop renormalization effect. Since the two-dimensional metric is locally conformally flat, the resulting effective theory is constructed in a flat space-time. We also construct tensorial operators (BRS, ghost number current and the energy momentum tensor) in the effective theory in a flat space-time based on anomalous Ward identities, i.e., trace, BRS and ghost number anomalies. Then we show that the effective theory has desired properties by calculating the operator product expansions. For example, we see that the total central charge of the Virasoro algebra vanishes. Our result forms a basis of a conformal field theoretical approach to two-dimensional quantum gravity and it has applications to a theory of non-critical strings. (author).
Authors:
Suzuki, Hiroshi [1] 
  1. Hiroshima Univ. (Japan). Dept. of Physics
Publication Date:
Jan 01, 1991
Product Type:
Technical Report
Report Number:
YITP/U-91-7
Reference Number:
SCA: 662110; PA: JPN-91:011022; SN: 92000630438
Resource Relation:
Other Information: PBD: Jan 1991
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM GRAVITY; CONFORMAL INVARIANCE; TWO-DIMENSIONAL CALCULATIONS; ENERGY-MOMENTUM TENSOR; METRICS; LAGRANGIAN FUNCTION; LAGRANGIAN FIELD THEORY; 662110; THEORY OF FIELDS AND STRINGS
OSTI ID:
10108980
Research Organizations:
Kyoto Univ., Uji (Japan). Yukawa Inst. for Theoretical Physics
Country of Origin:
Japan
Language:
English
Other Identifying Numbers:
Other: ON: DE92750831; TRN: JP9111022
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
JPN
Size:
35 p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Suzuki, Hiroshi. Conformal field theoretical approach to two-dimensional quantum gravity. Japan: N. p., 1991. Web.
Suzuki, Hiroshi. Conformal field theoretical approach to two-dimensional quantum gravity. Japan.
Suzuki, Hiroshi. 1991. "Conformal field theoretical approach to two-dimensional quantum gravity." Japan.
@misc{etde_10108980,
title = {Conformal field theoretical approach to two-dimensional quantum gravity}
author = {Suzuki, Hiroshi}
abstractNote = {A conformal (or Weyl) mode of two-dimensional gravity coupled to conformally invariant matter, which is a gauge degree of freedom in the classical level, becomes dynamical through the conformal (or Weyl) anomaly. We consider the BRS quantization of the above system in the conformal gauge. As a practical approach which enables us to do explicit calculations, we reduce the BRS invariant path integral measure for the conformal mode to the naive one by including a one-loop renormalization effect. Since the two-dimensional metric is locally conformally flat, the resulting effective theory is constructed in a flat space-time. We also construct tensorial operators (BRS, ghost number current and the energy momentum tensor) in the effective theory in a flat space-time based on anomalous Ward identities, i.e., trace, BRS and ghost number anomalies. Then we show that the effective theory has desired properties by calculating the operator product expansions. For example, we see that the total central charge of the Virasoro algebra vanishes. Our result forms a basis of a conformal field theoretical approach to two-dimensional quantum gravity and it has applications to a theory of non-critical strings. (author).}
place = {Japan}
year = {1991}
month = {Jan}
}