Gravité quantique et modèles de matrices

1991 ◽  
Vol 69 (7) ◽  
pp. 837-854 ◽  
Author(s):  
David Sénéchal
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Gravity ◽  
Orthogonal Polynomials ◽  
Matrix Models ◽  
Continuum Limit ◽  
Two Dimensional ◽  
Planar Approximation ◽  
Conformal Field ◽  
The Matrix

A review of the main results recently obtained in the study of two-dimensional quantum gravity is offered. The analysis of two-dimensional quantum gravity by the methods of conformal field theory is briefly described. Then the treatment of quantum gravity in terms of matrix models is explained, including the notions of continuum limit, planar approximation, and orthogonal polynomials. Correlation fonctions are also treated, as well as phases of the matrix models.

TWO-DIMENSIONAL QUANTUM GRAVITY ON A DISK

1992 ◽  
Vol 07 (06) ◽  
pp. 521-532 ◽  
Author(s):  
YOSHIAKI TANII ◽  
SHUN-ICHI YAMAGUCHI
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Gravity ◽  
Correlation Functions ◽  
Two Dimensional ◽  
Field Approach ◽  
Conformal Field ◽  
Boundary Operators ◽  
Point Correlation ◽  
The Continuum

We study a two-dimensional conformal field theory coupled to quantum gravity on a disk. Using the continuum Liouville field approach, we compute three-point correlation functions of boundary operators. The structure of momentum singularities is different from that of correlation functions on a sphere and is more complicated. We also compute four-point functions of boundary operators and three-point functions of two boundary operators and one bulk operator.

scholarly journals Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Suting Zhao ◽  
Christian Northe ◽  
René Meyer
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Gauge Field ◽  
Wilson Line ◽  
Entanglement Entropy ◽  
Simons Theory ◽  
Two Dimensional ◽  
Conformal Field ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We consider symmetry-resolved entanglement entropy in AdS3/CFT2 coupled to U(1) Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS3, namely the Ryu-Takayanagi geodesic minimally coupled to the U(1) Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged U(1) vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the U(1) Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincaré patch and global AdS3, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level k, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody type. Employing the $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.

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 ON THE CFT DUALS FOR NEAR-EXTREMAL BLACK HOLES

2011 ◽  
Vol 26 (22) ◽  
pp. 1601-1611 ◽  
Author(s):  
JØRGEN RASMUSSEN
Keyword(s):  
Field Theory ◽  
Black Holes ◽  
Black Hole ◽  
Conformal Field Theory ◽  
Two Dimensional ◽  
Conformal Field ◽  
Horizon Geometry ◽  
Cardy Formula ◽  
Asymptotic Symmetries ◽  
Extremal Black Holes

We consider Kerr–Newman–AdS–dS black holes near extremality and work out the near-horizon geometry of these near-extremal black holes. We identify the exact U (1)L× U (1)R isometries of the near-horizon geometry and provide boundary conditions enhancing them to a pair of commuting Virasoro algebras. The conserved charges of the corresponding asymptotic symmetries are found to be well-defined and nonvanishing and to yield central charges cL≠0 and cR = 0. The Cardy formula subsequently reproduces the Bekenstein–Hawking entropy of the black hole. This suggests that the near-extremal Kerr–Newman–AdS–dS black hole is holographically dual to a non-chiral two-dimensional conformal field theory.

Integrability in 2D fields theory/sigma-models

2019 ◽  
pp. 248-318
Author(s):  
Sergei L. Lukyanov ◽  
Alexander B. Zamolodchikov
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Sigma Models ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field ◽  
Zero Curvature ◽  
Basic Facts ◽  
Linear Sigma Models ◽  
General Aspects

This is a two-part course about the integrability of two-dimensional non-linear sigma models (2D NLSM). In the first part general aspects of classical integrability are discussed, based on the O(3) and O(4) sigma-models and the field theories related to them. The second part is devoted to the quantum 2D NLSM. Among the topics considered are: basic facts of conformal field theory, zero-curvature representations, integrals of motion, one-loop renormalizability of 2D NLSM, integrable structures in the so-called cigar and sausage models, and their RG flows. The text contains a large number of exercises of varying levels of difficulty.

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