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.

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 CONSTRUCTION OF AN IDENTICALLY NILPOTENT BRS CHARGE IN THE KATO–OGAWA STRING THEORY

1999 ◽  
Vol 14 (09) ◽  
pp. 1357-1377 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Field Equation ◽  
String Theory ◽  
Quantum Gravity ◽  
Bosonic Strings ◽  
Open String ◽  
Indefinite Metric ◽  
Two Dimensional ◽  
Conformal Gauge ◽  
Wightman Functions ◽  
Artificial Introduction

In previous work, the conformal-gauge two-dimensional quantum gravity in the BRS formalism has been solved completely in terms of Wightman functions. In the present paper, this result is extended to the closed and open bosonic strings of finite length; the open-string case is nothing but the Kato–Ogawa string theory. The field-equation anomaly found previously, which means a slight violation of a field equation at the level of Wightman functions, remains existent in the finite-string cases. By using this fact, a BRS charge nilpotent even for D≠26 is explicitly constructed in the framework of the Kato–Ogawa string theory. The FP-ghost vacuum structure of the Kato–Ogawa theory is made more transparent; the appearance of half-integral ghost numbers and the artificial introduction of an indefinite metric are avoided.

TWO DIMENSIONAL QUANTUM GRAVITY AND STRINGS

1990 ◽  
Vol 05 (10) ◽  
pp. 1833-1859 ◽  
Author(s):  
A.A. TSEYTLIN
Keyword(s):  
String Theory ◽  
Quantum Gravity ◽  
Conformal Factor ◽  
Target Space ◽  
Effective Theory ◽  
Two Dimensional ◽  
Conformal Gauge

We discuss some recent suggestions about a relation between 2-d quantum gravity and string theory. We consider the general 2-d σ model with D-dimensional target space coupled to 2-d quantum gravity and give arguments in favor of the conjecture that the effective theory which describes this system in the conformal gauge may be interpreted as a a model with a D+1-dimensional target space with the conformal factor of the metric playing the role of the D+1 coordinate. The latter σ model must be Weyl invariant while the original one may be arbitrary. The conformal “split” invariance which must be present in the conformal gauge imposes no restrictions on the original σ model couplings, but restricts the additional (D+1-dimensional) couplings which appear in the D+1-dimensional σ model.

scholarly journals D = 26 AND EXACT SOLUTION TO THE CONFORMAL-GAUGE TWO-DIMENSIONAL QUANTUM GRAVITY

1999 ◽  
Vol 14 (04) ◽  
pp. 521-536 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Exact Solution ◽  
Field Equation ◽  
Quantum Gravity ◽  
Critical Dimension ◽  
Bosonic String ◽  
Ghost Number ◽  
Conformal Anomaly ◽  
Two Dimensional ◽  
Heisenberg Picture ◽  
Conformal Gauge

The conformal-gauge two-dimensional quantum gravity is formulated in the framework of the BRS quantization and solved completely in the Heisenberg picture: all n-point Wightman functions are explicitly obtained. The field-equation anomaly is shown to exist as in other gauges, but there is no other subtlety. At the critical dimension D = 26 of the bosonic string, the field-equation anomaly is shown to be absent. However, this result is not equivalent to the statement that the conformal anomaly is proportional to D - 26. The existence of the FP-ghost number current anomaly is seen to be an illusion.

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.

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