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.

ON THE ALGEBRAIC STRUCTURE of QUANTUM GRAVITY IN TWO DIMENSIONS

1991 ◽  
Vol 06 (16) ◽  
pp. 2805-2827 ◽  
Author(s):  
Jean-Loup Gervais
Keyword(s):  
Quantum Gravity ◽  
Quantum Group ◽  
Algebraic Structure ◽  
Group Structure ◽  
Two Dimensions ◽  
Conformal Gauge

Current progresses in understanding quantum gravity from the operator viewpoint are reviewed. They are based on the Uq(sl(2))-quantum-group structure recently put forward1,2, for the chiral components of the metric in the conformal gauge.

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.

A COMPACT BOSON COUPLED TO TWO-DIMENSIONAL GRAVITY

1991 ◽  
Vol 06 (15) ◽  
pp. 2743-2754 ◽  
Author(s):  
NORISUKE SAKAI ◽  
YOSHIAKI TANII
Keyword(s):  
Field Theory ◽  
Partition Function ◽  
Quantum Gravity ◽  
Matrix Models ◽  
Riemann Surfaces ◽  
Partition Functions ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
The Continuum ◽  
Continuum Field

The radius dependence of partition functions is explicitly evaluated in the continuum field theory of a compactified boson, interacting with two-dimensional quantum gravity (noncritical string) on Riemann surfaces for the first few genera. The partition function for the torus is found to be a sum of terms proportional to R and 1/R. This is in agreement with the result of a discretized version (matrix models), but is quite different from the critical string. The supersymmetric case is also explicitly evaluated.

POISSON–LIE GROUPS AND CLASSICAL W-ALGEBRAS

1992 ◽  
Vol 07 (05) ◽  
pp. 853-876 ◽  
Author(s):  
V. A. FATEEV ◽  
S. L. LUKYANOV
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Group ◽  
Lie Groups ◽  
Group Structure ◽  
Two Dimensional ◽  
Poisson Structures ◽  
Additional Symmetries ◽  
Conformal Field ◽  
Poisson Lie Groups

This is the first part of a paper studying the quantum group structure of two-dimensional conformal field theory with additional symmetries. We discuss the properties of the Poisson structures possessing classical W-invariance. The Darboux variables for these Poisson structures are constructed.

Two-dimensional quantum gravity in the conformal gauge

1990 ◽  
Vol 42 (4) ◽  
pp. 1144-1146 ◽  
Author(s):  
Chang Jun Ahn ◽  
Young Jai Park ◽  
Kee Yong Kim ◽  
Yongduk Kim ◽  
Won Tae Kim ◽  
...  
Keyword(s):  
Quantum Gravity ◽  
Two Dimensional ◽  
Conformal Gauge

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.

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.

FROM LOOPS TO FIELDS IN 2D QUANTUM GRAVITY

1992 ◽  
Vol 07 (11) ◽  
pp. 2601-2634 ◽  
Author(s):  
GREGORY MOORE ◽  
NATHAN SEIBERG
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Zero Mode ◽  
Integral Transform ◽  
Target Space ◽  
Two Dimensional ◽  
And Topology ◽  
The Matrix ◽  
Dimensional Gravity ◽  
Infinite Set

We discuss a target space field theory of macroscopic loops W(ℓ,…) in two-dimensional gravity. The propagator <W(ℓ1)W(ℓ2)> and topology-changing amplitudes <W(ℓ1)W(ℓ2)W(ℓ3)> (string interactions) are considered as off-shell Euclidean Green's functions in this field theory. In the course of the analysis, we identify a new set of operators in the c = 1 system and interpret them in two-dimensional gravity. We also identify an infinite set of new conserved charges in the c = 1 system which are associated with the special states in the theory. The analysis also shows that the eigenvalue coordinate of the matrix model and a zero mode of the Liouville field are not functionally related but are conjugate variables in an integral transform.

Sign in / Sign up

Export Citation Format

Share Document