Two-dimensional gravity: quantum group structure of the continuum theory

1992 ◽  
Vol 9 (S) ◽  
pp. S97-S116 ◽  
Author(s):  
J -L Gervais
Keyword(s):  
Quantum Group ◽  
Group Structure ◽  
Continuum Theory ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
The Continuum

TETRACRITICAL ISING MODEL COUPLED TO THE TWO-DIMENSIONAL GRAVITY

1992 ◽  
Vol 07 (19) ◽  
pp. 4487-4499
Author(s):  
ALOK KUMAR ◽  
JNANADEVA MAHARANA
Keyword(s):  
Ising Model ◽  
Central Charge ◽  
Continuum Theory ◽  
Two Dimensional ◽  
Operator Approach ◽  
Modular Invariant ◽  
Lax Operator ◽  
Dimensional Gravity ◽  
Ade Classification ◽  
The Continuum

Nonperturbative string equations are found explicitly for a central charge c=4/5 model coupled to the two-dimensional quantum gravity in the Lax operator approach proposed by Douglas. These string equations are used to derive the scaling behavior of several correlation functions on the sphere and it is shown that they agree with the calculations of the continuum theory. The model, identified with the diagonal modular invariant in the ADE classification, corresponds to the tetracritical Ising model.

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.

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.

scholarly journals The continuum theory of shear localization in two-dimensional foam

2010 ◽  
Vol 22 (19) ◽  
pp. 193101 ◽  
Author(s):  
Denis Weaire ◽  
Joseph D Barry ◽  
Stefan Hutzler
Keyword(s):  
Continuum Theory ◽  
Shear Localization ◽  
Two Dimensional ◽  
The Continuum

scholarly journals Operator coproduct-realization of quantum group transformations in two-dimensional gravity I

1996 ◽  
Vol 178 (1) ◽  
pp. 147-177
Author(s):  
Eugène Cremmer ◽  
Jean-Loup Gervais ◽  
Jens Schnittger
Keyword(s):  
Quantum Group ◽  
Two Dimensional ◽  
Dimensional Gravity

scholarly journals Nonlinear and Nonlocal Elasticity in Coarse-Grained Differential-Tension Models of Epithelia

2018 ◽  
Author(s):  
Haas Pierre A. ◽  
Goldstein Raymond E.
Keyword(s):  
Nonlocal Elasticity ◽  
Continuum Theory ◽  
Coarse Grained ◽  
Elastic Behavior ◽  
Two Dimensional ◽  
Adhesion Forces ◽  
Cell Level ◽  
Complex Interplay ◽  
Contractile Forces ◽  
The Continuum

The shapes of epithelial tissues result from a complex interplay of contractile forces in the cytoskeleta of the cells in the tissue, and adhesion forces between them. A host of discrete, cell-based models describe these forces by assigning different surface tensions to the apical, basal, and lateral sides of the cells. These differential-tension models have been used to describe the deformations of epithelia in different living systems, but the underlying continuum mechanics at the scale of the epithelium are still unclear. Here, we derive a continuum theory for a simple differential-tension model of a two-dimensional epithelium and study the buckling of this epithelium under imposed compression. The analysis reveals howthe cell-level properties encoded in the differential-tension model lead to linear, nonlinear as well as nonlocal elastic behavior at the continuum level.

scholarly journals QUANTUM GROUP SYMMETRY AND QUANTUM HALL WAVE FUNCTIONS ON A TORUS

1994 ◽  
Vol 09 (20) ◽  
pp. 1819-1825 ◽  
Author(s):  
HARU-TADA SATO
Keyword(s):  
Quantum Group ◽  
Uniform Magnetic Field ◽  
Deformation Parameter ◽  
Filling Factor ◽  
Particle System ◽  
Group Structure ◽  
Quantum Hall ◽  
Wave Functions ◽  
Group Symmetry ◽  
Two Dimensional

We generalize the quantum group structure of two-dimensional nonrelativistic electron in a uniform magnetic field into the case of a many-particle system on a torus. We verify the conjecture that the deformation parameter of the quantum algebra is given by the filling factor ν=1/p (p odd) on the basis of the Haldane-Rezayi’s wave functions.

scholarly journals Hidden U q (sl(2)) $otimes$ U q (sl(2)) Quantum Group Symmetry in Two Dimensional Gravity

1997 ◽  
Vol 183 (3) ◽  
pp. 609-643 ◽  
Author(s):  
Eugène Cremmer ◽  
Jean-Loup Gervais ◽  
Jens Schnittger
Keyword(s):  
Quantum Group ◽  
Group Symmetry ◽  
Two Dimensional ◽  
Dimensional Gravity
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