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.

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.

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.

SEMICLASSICAL TWO-DIMENSIONAL GRAVITY IN LIGHT-CONE GAUGE

1989 ◽  
Vol 04 (05) ◽  
pp. 419-425 ◽  
Author(s):  
R. FLOREANINI
Keyword(s):  
Light Cone ◽  
Einstein Equations ◽  
Two Dimensional ◽  
Light Cone Gauge ◽  
Dimensional Gravity ◽  
Conformal Gauge

Semiclassical Einstein equations for two-dimensional gravity are investigated in lightcone gauge and their group of invariance is discussed. One finds differences with respect to the corresponding results in conformal gauge.

AN INTEGRABLE MODEL WITH SOLITON SOLUTIONS WHICH HAVE APPLICATIONS TO TWO-DIMENSIONAL GRAVITY

2005 ◽  
Vol 20 (07) ◽  
pp. 1503-1514 ◽  
Author(s):  
PAUL BRACKEN
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Integrable Model ◽  
Soliton Solutions ◽  
Integrable Equation ◽  
Two Dimensions ◽  
Spin Connection ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
Chern Simons

The equations of motion for a theory described by a Chern–Simons type of action in two dimensions are obtained and investigated. The equation for the classical, continuous Heisenberg model is used as a form of gauge constraint to obtain a result which provides a completely integrable dynamics and which partially fixes the gauge degrees of freedom. Under a particular form of the spin connection, an integrable equation which can be analytically extended to a form of the nonlinear Schrödinger equation is obtained. Some explicit solutions are presented, and in particular a soliton solution is shown to lead to an integrable two-dimensional model of gravity.

scholarly journals CANONICAL TREATMENT OF TWO-DIMENSIONAL GRAVITY AS AN ANOMALOUS GAUGE THEORY

1993 ◽  
Vol 08 (23) ◽  
pp. 2147-2154 ◽  
Author(s):  
T. FUJIWARA ◽  
T. TABEI ◽  
Y. IGARASHI ◽  
K. MAEDA ◽  
J. KUBO
Keyword(s):  
Brst Symmetry ◽  
Extended Phase Space ◽  
Two Dimensional ◽  
Extended Phase ◽  
Light Cone Gauge ◽  
Gauge Action ◽  
Dimensional Gravity ◽  
Conformal Gauge ◽  
The Relationship ◽  
Space Method

The extended phase space method of Batalin, Fradkin and Vilkovisky is applied to formulate two-dimensional gravity in a general class of gauges. A BRST formulation of the light-cone gauge is presented to reveal the relationship between the BRST symmetry and the origin of SL (2, ℝ) current algebra. From the same principle we derive the conformal gauge action suggested by David, Distler and Kawai.

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.

scholarly journals LAX-PAIR FORMULATION OF THE W-GRAVITY THEORIES IN TWO DIMENSIONS

1992 ◽  
Vol 07 (27) ◽  
pp. 6907-6932 ◽  
Author(s):  
LINA JEAN-MARC ◽  
PRASANTA K. PANIGRAHI
Keyword(s):  
Light Cone ◽  
2D Gravity ◽  
Lax Pair ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Curvature Condition ◽  
Induced Gravity ◽  
Light Cone Gauge ◽  
Zero Curvature ◽  
Cosmological Constants

The Lax-pair formulation of the two-dimensional induced gravity in the light-cone gauge is extended to the more general wN theories. After presenting the w2 and w3 gravities, we give a general prescription for an arbitrary wN case. This is further illustrated with the w4 gravity to point out some peculiarities. The constraints and the possible presence of the cosmological constants are systematically exhibited in the zero-curvature condition, which also yields the relevant Ward identities. The restrictions on the gauge parameters in the presence of the constraints are pointed out too, and are contrasted with those of the ordinary 2D gravity.

LAX PAIR AND COSMOLOGICAL CONSTANT FOR INDUCED 2D-GRAVITY IN THE LIGHT-CONE GAUGE

1991 ◽  
Vol 06 (38) ◽  
pp. 3517-3524 ◽  
Author(s):  
JEAN-MARC LINA ◽  
PRASANTA K. PANIGRAHI
Keyword(s):  
Cosmological Constant ◽  
Light Cone ◽  
2D Gravity ◽  
Lax Pair ◽  
Two Dimensional ◽  
Classical Level ◽  
Induced Gravity ◽  
Light Cone Gauge ◽  
Special Solutions ◽  
Cosmological Constants

We present the Lax pair to describe the two-dimensional induced gravity in the light-cone gauge. This is done at the classical level, with the cosmological constant which so far has not been accounted for in this context. The symmetries are discussed, together with some solutions of the integrability conditions. The case of the W3 gravity is also analyzed; exhibiting some special solutions and highlighting the roles of the two cosmological constants in its Lax pair formulation.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

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