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.

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.

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.

RENORMALIZATION OF TWO-DIMENSIONAL SUPERGRAVITY IN LIGHT-CONE GAUGE

1990 ◽  
Vol 05 (02) ◽  
pp. 125-131
Author(s):  
ANAIS SMAILAGIC
Keyword(s):  
Wave Function ◽  
Current Algebra ◽  
Light Cone ◽  
Central Charge ◽  
Two Dimensional ◽  
Perturbative Calculation ◽  
Light Cone Gauge ◽  
D Region

Perturbative calculation of two-dimensional (1, 0) supergravity due to gravitation fluctuations is performed. Renormalization of Kac-Moody central charge of SL(2, R) graded current algebra and wave function to one-loop is obtained. The result agrees perfectly with Polyakov’s formula in the large d region.

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 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.

SYMMETRY REORGANIZATION IN EXACTLY SOLVABLE TWO-DIMENSIONAL QUANTIZED SUPERGRAVITY

1989 ◽  
Vol 04 (09) ◽  
pp. 2245-2272 ◽  
Author(s):  
N.D. HARI DASS ◽  
R. SUMITRA
Keyword(s):  
Correlation Functions ◽  
Light Cone ◽  
Quantum Correlation ◽  
Two Dimensional ◽  
Supergravity Theory ◽  
Light Cone Gauge ◽  
Infinite Dimensional ◽  
Diffeomorphism Invariance ◽  
Supersymmetric Version ◽  
Exactly Solvable

A recent work of Polyakov solving exactly the two-dimensional induced quantum gravity is extended to the two-dimensional induced (1,0) quantum supergravity theory. This theory is found to be exactly integrable in a supersymmetric version of the light cone gauge. Solutions are found to display an infinite dimensional Z2 graded sl(2, R) invariance and a diffeomorphism invariance in one of the coordinates. The origin of these invariances is traced to motions along the gauge slice. A Sugawara construction based on the currents of the infinite dimensional transformations is shown to generate these diffeomorphisms. Explicit results are given for a number of quantum correlation functions.

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.

scholarly journals Quantum gravity as a multitrace matrix model

2017 ◽  
Vol 32 (31) ◽  
pp. 1750180
Author(s):  
Badis Ydri ◽  
Cherine Soudani ◽  
Ahlam Rouag
Keyword(s):  
Quantum Gravity ◽  
Matrix Models ◽  
Large Class ◽  
Matrix Model ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Topology Change ◽  
New Model ◽  
And Topology ◽  
Emergent Geometry

We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of two-dimensional quantum gravity which works away from two dimensions and captures a large class of spaces admitting a finite spectral triple. These multitrace matrix models sustain emergent geometry as well as growing dimensions and topology change.

Sign in / Sign up

Export Citation Format

Share Document