scholarly journals HUGE SPACE-DEPENDENT SYMMETRY IN THE LIGHTCONE GAUGE TWO-DIMENSIONAL QUANTUM GRAVITY

1996 ◽  
Vol 11 (15) ◽  
pp. 2623-2642 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Quantum Gravity ◽  
Current Algebra ◽  
Symmetry Algebra ◽  
Local Version ◽  
Two Dimensional ◽  
Operator Formalism ◽  
Canonical Operator ◽  
Coordinate Invariance

The lightcone gauge two-dimensional quantum gravity, i.e. the local version of Polyakov’s “induced” quantum gravity, is analyzed in the canonical operator formalism. An extremely huge x+-dependent symmetry algebra is found to exist in this model. Both Polyakov’s SL (2, R) current algebra and residual general coordinate invariance are very very tiny subalgebras of it.

COVARIANT OPERATOR FORMALISM OF TWO-DIMENSIONAL TOPOLOGICAL GRAVITY

1992 ◽  
Vol 07 (13) ◽  
pp. 3105-3131
Author(s):  
NORIAKI IKEDA
Keyword(s):  
Quantum Gravity ◽  
Two Dimensional ◽  
Operator Formalism ◽  
Canonical Operator ◽  
Covariant Operator ◽  
Gauge Fixing ◽  
Topological Gravity

The manifestly covariant canonical operator formalism of two-dimensional topological gravity is formulated. Its unitarity is confirmed by means of constructing the Kugo–Ojima's quartets. A number of new symmetries are found by adopting a particular gauge fixing condition. These symmetries correspond to the "choral symmetry" generated by the 4N-dimensional Poincaré-like superalgebra in the ordinary N-dimensional quantum gravity.

UNITARY THEORY OF TWO-DIMENSIONAL QUANTUM GRAVITY AND ITS EXACT COVARIANT OPERATOR SOLUTION

1991 ◽  
Vol 06 (22) ◽  
pp. 3955-3971 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Quantum Gravity ◽  
Two Dimensional ◽  
Operator Formalism ◽  
Unitary Theory ◽  
Operator Solution ◽  
Canonical Operator ◽  
Weyl Invariance ◽  
Covariant Operator ◽  
Gauge Fixing

The manifestly covariant canonical operator formalism of two-dimensional quantum gravity is formulated on the basis of Sato’s gauge-fixing of the Weyl invariance. The unitarity problem, due to ghost-counting mismatch, is resolved by making the gravitational FP ghosts also play the role of the Weyl FP ghosts. All two-dimensional (anti)commutators between fundamental fields are explicitly 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.

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.

Two-dimensional quantum gravity and current algebra on a torus

1990 ◽  
Vol 240 (3-4) ◽  
pp. 341-344
Author(s):  
Jung-Jai Lee ◽  
Won-Sang Chung ◽  
Sin-Kyu Kang ◽  
Jae-Kwan Kim
Keyword(s):  
Quantum Gravity ◽  
Current Algebra ◽  
Two Dimensional
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