Conformal field theory and 2D quantum gravity

Distler, Jacques; Kawai, Hiroyuki

doi:10.1016/0550-3213(89)90354-4

Cited by 1,059 publications

(815 citation statements)

References 23 publications

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“…On the other hand under Virasoro transformations parametrized by (x + ) we have 14) where c = 3l/2G. Thus, we find that in the semiclassical limit the central charge of the matter plus ghost systems is given by the Brown-Henneaux central charge, 15) and, using eq.…”

Section: Jhep03(2014)116mentioning

confidence: 91%

“…Weyl scalings, receive gravitational corrections. In particular, the gravitationally-dressed weights of scalar primary fields are given by [13,14] …”

Section: Jhep03(2014)116mentioning

confidence: 99%

“…(1.4), since the Polyakov action reduces to the Liouville action where ϕ is conformally-coupled. The Polyakov action is required for consistency of the theory [12][13][14][15]. It guarantees that the Ward identities of the theory, which are sensitive to anomalous contributions from the measure, are realized at the classical level.…”

Section: Jhep03(2014)116mentioning

confidence: 99%

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Free boundary conditions and the AdS3/CFT2 correspondence

Apolo

Porrati

2014

J. High Energ. Phys.

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We show that recently proposed free boundary conditions for AdS 3 are dual to two-dimensional quantum gravity in certain fixed gauges. In particular, we note that an appropriate identification of the generator of Virasoro transformations leads to a vanishing total central charge in agreement with the theory at the boundary. We argue that this identification is necessary to match the bulk and boundary generators of Virasoro transformations and for consistency with the constraint equations.

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Section: Jhep03(2014)116mentioning

confidence: 91%

“…Weyl scalings, receive gravitational corrections. In particular, the gravitationally-dressed weights of scalar primary fields are given by [13,14] …”

Section: Jhep03(2014)116mentioning

confidence: 99%

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Free boundary conditions and the AdS3/CFT2 correspondence

Apolo

Porrati

2014

J. High Energ. Phys.

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“…This was to be expected since what we find is the usual link between the rg-flow equations and the conformal condition typical of a Liouville dressing (see e.g [1,2,33,35]). This identification holds, however, only in the large-Q regime.…”

Section: Jhep01(2007)040mentioning

confidence: 99%

“…2 The one-loop Weyl-invariance equations are satisfied for the full (d + 1)-dimensional space-time provided a background dilaton is also switched on in the time direction. In the case of the three-sphere, we generalize the time warping by implementing time dependence in all three parameters that were studied in the rg approach -anisotropic warping.…”

Section: Jhep01(2007)040mentioning

confidence: 99%

Ricci flows and expansion in axion-dilaton cosmology

Bakas

Orlando

Petropoulos

2007

J. High Energy Phys.

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We study renormalization-group flows by deforming a class of conformal sigmamodels. We consider overall scale factor perturbation of Einstein spaces as well as more general anisotropic deformations of three-spheres. At leading order in α , renormalizationgroup equations turn out to be Ricci flows. In the three-sphere background, the latter is the Halphen system, which is exactly solvable in terms of modular forms. We also analyze time-dependent deformations of these systems supplemented with an extra time coordinate and time-dependent dilaton. In some regimes time evolution is identified with renormalization-group flow and time coordinate can appear as Liouville field. The resulting space-time interpretation is that of a homogeneous isotropic Friedmann-Robertson-Walker universe in axion-dilaton cosmology. We find as general behaviour the superposition of a big-bang (polynomial) expansion with a finite number of oscillations at early times. Any initial anisotropy disappears during the evolution.

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Introduction to Nonperturbative 2D Quantum Gravity

Lozano¹,

Mañes²

1993

Fortschr. Phys.

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We give an elementary introduction to the theory of matrix models, as applied to the study of 2 D quantum gravity. Starting from the sum over surfaces, we explain carefully the steps leading to the non-perturbative solution: discretization, duality, diagram-counting techniques, 1/N expansion, double-scaling limit, etc. Many examples are worked out in detail, and a pedagogical discussion of the concepts of universality and the non-perturbative ambiguity is presented.

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Conformal field theory and 2D quantum gravity

Cited by 1,059 publications

References 23 publications

Free boundary conditions and the AdS3/CFT2 correspondence

Free boundary conditions and the AdS3/CFT2 correspondence

Ricci flows and expansion in axion-dilaton cosmology

Introduction to Nonperturbative 2D Quantum Gravity

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