CANONICAL DESCRIPTION OF A TWO-DIMENSIONAL GRAVITY

1992 ◽  
Vol 07 (19) ◽  
pp. 1757-1764 ◽  
Author(s):  
K.G. AKDENIZ ◽  
Ö.F. DAYI ◽  
A. KIZILERSÜ
Keyword(s):  
Degrees Of Freedom ◽  
Mass Shell ◽  
Gravity Theory ◽  
Two Dimensional ◽  
Lagrangian Methods ◽  
Hamiltonian Methods ◽  
Dimensional Gravity ◽  
Conformal Gauge

A two-dimensional gravity theory which was studied before within the Lagrangian methods, in the conformal gauge is investigated in terms of the Hamiltonian methods. Although the reparametrization invariant and the conformal gauge fixed Lagrangians lead to different number of physical degrees of freedom, it is shown that on mass-shell they are equivalent.

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.

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.

INTERSECTION THEORY AND TWO-DIMENSIONAL GRAVITY AT GENUS 3 AND 4

1990 ◽  
Vol 05 (26) ◽  
pp. 2127-2134 ◽  
Author(s):  
JAMES H. HORNE
Keyword(s):  
Moduli Space ◽  
Intersection Theory ◽  
Gravity Theory ◽  
Two Dimensional ◽  
Intersection Numbers ◽  
Dimensional Gravity

We show that the k = 1 two-dimensional gravity amplitudes at genus 3 agree precisely with the results from intersection theory on moduli space. Predictions for the genus 4 intersection numbers follow easily from the two-dimensional gravity theory.

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.

TWO-DIMENSIONAL GRAVITY WITH BOUNDARY

1992 ◽  
Vol 07 (07) ◽  
pp. 619-629
Author(s):  
PARTHASARATHI MAJUMDAR
Keyword(s):  
Boundary Conditions ◽  
Central Charge ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
Conformal Gauge

An attempt is made to incorporate the effects of a boundary in the conformal gauge solution of two-dimensional gravity. We discuss some possible choices for boundary conditions on the Liouville field and their implications for the renormalization of the central charge.

DYNAMICAL TIME VARIABLE IN COSMOLOGY

1988 ◽  
Vol 03 (04) ◽  
pp. 333-343
Author(s):  
TAKESHI FUKUYAMA ◽  
KIYOSHI KAMIMURA
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Time Variable ◽  
Gravity Theory ◽  
Two Dimensional ◽  
Maximum Radius ◽  
Dynamical Time ◽  
Dimensional Gravity ◽  
Time Variables ◽  
The Universe

Dynamical time variables are studied in two dimensional gravity theory. Dynamical time and space variables exchange their role at the maximum radius (amax) like a black hole at event horizon. Dynamical arrows of time are directed towards amax in both expanding and contracting phases. Both time flows cannot go beyond amax, and the universe becomes static at amax.

QUANTUM GROUP AND TWO-DIMENSIONAL GRAVITY

1992 ◽  
Vol 06 (11n12) ◽  
pp. 1917-1937 ◽  
Author(s):  
JEAN-LOUP GERVAIS
Keyword(s):  
Quantum Gravity ◽  
Quantum Group ◽  
Group Structure ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
Conformal Gauge

Current progress in understanding quantum gravity from the operator viewpoint are reviewed. They are based on the Uq(sl(2))-quantum-group structure recently put forward,1,2 for the chiral components of the metric in the conformal gauge.

scholarly journals Developments in topological gravity

2018 ◽  
Vol 33 (30) ◽  
pp. 1830029 ◽  
Author(s):  
Robbert Dijkgraaf ◽  
Edward Witten
Keyword(s):  
Matrix Model ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Degrees Of Freedom ◽  
Intersection Theory ◽  
Two Dimensional ◽  
The Matrix ◽  
Dimensional Gravity ◽  
Topological Gravity ◽  
The Relationship

This note aims to provide an entrée to two developments in two-dimensional topological gravity — that is, intersection theory on the moduli space of Riemann surfaces — that have not yet become well known among physicists. A little over a decade ago, Mirzakhani discovered[Formula: see text] an elegant new proof of the formulas that result from the relationship between topological gravity and matrix models of two-dimensional gravity. Here we will give a very partial introduction to that work, which hopefully will also serve as a modest tribute to the memory of a brilliant mathematical pioneer. More recently, Pandharipande, Solomon, and Tessler3 (with further developments in Refs. 4–6) generalized intersection theory on moduli space to the case of Riemann surfaces with boundary, leading to generalizations of the familiar KdV and Virasoro formulas. Though the existence of such a generalization appears natural from the matrix model viewpoint — it corresponds to adding vector degrees of freedom to the matrix model — constructing this generalization is not straightforward. We will give some idea of the unexpected way that the difficulties were resolved.

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