EQUIVALENCE OF LIGHT-CONE AND CONFORMAL GAUGES IN TWO-DIMENSIONAL QUANTUM GRAVITY

1992 ◽  
Vol 07 (25) ◽  
pp. 2263-2268 ◽  
Author(s):  
CHANG-JUN AHN ◽  
WON-TAE KIM ◽  
YOUNG-JAI PARK ◽  
KEE YONG KIM ◽  
YONGDUK KIM
Keyword(s):  
Scalar Field ◽  
Quantum Gravity ◽  
Coordinate Transformation ◽  
Light Cone ◽  
Two Dimensional ◽  
Light Cone Gauge ◽  
Current Structure ◽  
Residual Symmetry

We show that the light-cone and conformal gauges are equivalent in the sense that the well known SL (2, ℝ) current structure in the light-cone gauge is obtained from the results in the conformal one under a proper coordinate transformation. This result is due to the residual symmetry of the scalar field Φ.

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.

QUANTUM GRAVITY IN TWO DIMENSIONS

1987 ◽  
Vol 02 (11) ◽  
pp. 893-898 ◽  
Author(s):  
A. M. POLYAKOV
Keyword(s):  
Differential Equations ◽  
Quantum Gravity ◽  
Current Algebra ◽  
Correlation Functions ◽  
Light Cone ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Light Cone Gauge

Two dimensional induced quantum gravity is analyzed. By the use of light-cone gauge we derive a gravitational analogue of the Wess-Zumino action and discover its amazing connection with SL (2, ℝ) current algebra. The latter permits us to find differential equations for the correlation functions.

scholarly journals Consistent Two-Dimensional Chiral Gravity

1997 ◽  
Vol 12 (21) ◽  
pp. 3695-3722
Author(s):  
A. Smailagic ◽  
E. Spallucci
Keyword(s):  
Symmetry Group ◽  
Critical Exponents ◽  
Light Cone ◽  
Central Charge ◽  
Two Dimensional ◽  
Induced Gravity ◽  
Light Cone Gauge ◽  
Residual Symmetry ◽  
Vacuum States ◽  
Forbidden Region

We study chiral induced gravity in the light-cone gauge and show that the theory is consistent for a particular choice of chiralities. The corresponding Kac–Moody central charge has no forbidden region of complex values. Generalized analysis of the critical exponents is given and their relation to the SL (2,R) vacuum states is elucidated. All the parameters containing information about the theory can be traced back to the characteristics of the residual symmetry group in the light-cone gauge.

INDUCED TWO-DIMENSIONAL QUANTUM GRAVITY WITH GENERAL ACTION

1991 ◽  
Vol 06 (34) ◽  
pp. 3191-3197 ◽  
Author(s):  
S. D. ODINTSOV
Keyword(s):  
Quantum Gravity ◽  
Current Algebra ◽  
Light Cone ◽  
Two Dimensional ◽  
Light Cone Gauge ◽  
General Action ◽  
Non Local

The two-dimensional quantum gravity with general action consisting of local and non-local parts is investigated. It is shown that in the light-cone gauge there exists a symmetry which leads naturally to the SL (2,ℝ) Kac–Moody current algebra. The structure of the renormalization is discussed.

ON THE BRST APPROACH TO TWO-DIMENSIONAL GAUGE THEORIES IN THE LIGHT-CONE GAUGE

1990 ◽  
Vol 05 (12) ◽  
pp. 927-933 ◽  
Author(s):  
YOSHIAKI TANII
Keyword(s):  
Scalar Field ◽  
Gauge Field ◽  
Physical Meaning ◽  
Light Cone ◽  
Gauge Theories ◽  
Two Dimensional ◽  
Light Cone Gauge ◽  
Brst Charge

The physical meaning of the second BRST-like charge, which exists in addition to the ordinary BRST charge in two-dimensional gauge theories in the light-cone gauge, is clarified. It results from the redundancy of the parametrization of the gauge field in terms of a group-valued scalar field and has a similar structure to the ordinary one.

TOPOLOGICAL CONFORMAL ALGEBRA IN POLYAKOV’S LIGHT-CONE GAUGE GRAVITY

1992 ◽  
Vol 07 (35) ◽  
pp. 3291-3302 ◽  
Author(s):  
KIYONORI YAMADA
Keyword(s):  
Light Cone ◽  
Matter Field ◽  
Conformal Algebra ◽  
Two Dimensional ◽  
Topological Algebras ◽  
Light Cone Gauge ◽  
Brst Cohomology ◽  
Dimensional Gravity ◽  
Conformal Gauge ◽  
Gauge Gravity

We show that the two-dimensional gravity coupled to c=−2 matter field in Polyakov’s light-cone gauge has a twisted N=2 superconformal algebra. We also show that the BRST cohomology in the light-cone gauge actually coincides with that in the conformal gauge. Based on this observation the relations between the topological algebras are discussed.

EQUIVALENCE OF TWO-DIMENSIONAL GRAVITIES

1990 ◽  
Vol 05 (16) ◽  
pp. 1251-1258 ◽  
Author(s):  
NOUREDDINE MOHAMMEDI
Keyword(s):  
Gauge Theory ◽  
Explicit Solution ◽  
Light Cone ◽  
Equations Of Motion ◽  
Two Dimensional ◽  
Induced Gravity ◽  
Light Cone Gauge ◽  
Dimensional Gravity ◽  
The Relationship ◽  
Chern Simons

We find the relationship between the Jackiw-Teitelboim model of two-dimensional gravity and the SL (2, R) induced gravity. These are shown to be related to a two-dimensional gauge theory obtained by dimensionally reducing the Chern-Simons action of the 2+1 dimensional gravity. We present an explicit solution to the equations of motion of the auxiliary field of the Jackiw-Teitelboim model in the light-cone gauge. A renormalization of the cosmological constant is also given.

SYMMETRY IN TWO-DIMENSIONAL GRAVITY

1991 ◽  
Vol 06 (13) ◽  
pp. 2331-2346 ◽  
Author(s):  
KAI-WEN XU ◽  
CHUAN-JIE ZHU
Keyword(s):  
Light Cone ◽  
Integration Method ◽  
Symmetry Algebra ◽  
Two Dimensional ◽  
Light Cone Gauge ◽  
Simple Interpretation ◽  
Brst Charge ◽  
Dimensional Gravity ◽  
Covariant Gauge ◽  
Liouville Action

We study the symmetry of two-dimensional gravity by choosing a generic gauge. A local action is derived which reduces to either the Liouville action or the Polyakov one by reducing to the conformal or light-cone gauge respectively. The theory is also solved classically. We show that an SL (2, R) covariant gauge can be chosen so that the two-dimensional gravity has a manifest Virasoro and the sl (2, R)-current symmetry discovered by Polyakov. The symmetry algebra of the light-cone gauge is shown to be isomorphic to the Beltrami algebra. By using the contour integration method we construct the BRST charge QB corresponding to this algebra following the Fradkin-Vilkovisky procedure and prove that the nilpotence of QB requires c=28 and α0=1. We give a simple interpretation of these conditions.

scholarly journals A NOTE ON 2D CHIRAL GRAVITY AND CHIRAL BOSONS

1992 ◽  
Vol 07 (40) ◽  
pp. 3777-3782 ◽  
Author(s):  
FIORENZO BASTIANELLI
Keyword(s):  
Effective Action ◽  
Light Cone ◽  
Two Dimensional ◽  
Light Cone Gauge ◽  
Conformal Gauge ◽  
Chiral Bosons

Quantization of two-dimensional chiral matter coupled to gravity induces an effective action for the zweibein field which is both Weyl and Lorentz anomalous. Recently, the quantization of this induced action has been analyzed in the light-cone gauge as well as in the conformal gauge. An apparent mismatch between the results obtained in the two gauges is analyzed and resolved by properly treating the Lorentz field as a chiral boson.

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