2-d gravity and matrix models. 1. 2-d gravity

gravity developed for the last years are reviewed. They are physical (Liouville) gravity, topological theories and matrix models. A special attention is paid to matrix models and their interrelations with different approaches. Almost all technical details are omitted, but examples are presented.

lectures: Zelenogorsk 1993/02/18
gravitation
dimension: 2
matrix model: Kontsevich model
field theory: Liouville
field theory: topological
integrability
constraint: Virasoro
continuum limit
differential equations: string

References(90)

Figures(0)

Quantum Geometry of Bosonic Strings

Alexander M. Polyakov
(
- Landau Inst.
)

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Quantum Geometry of Fermionic Strings

Alexander M. Polyakov
(
- Landau Inst.
)

- Phys.Lett.B 103 (1981) 211-213,
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Fractal Structure of 2D Quantum Gravity

V.G. Knizhnik
(
- Landau Inst.
)
,
Alexander M. Polyakov
(
- Landau Inst.
)
,
A.B. Zamolodchikov
(
- Landau Inst.
)

- Mod.Phys.Lett.A 3 (1988) 819,
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Conformal Field Theories Coupled to 2D Gravity in the Conformal Gauge

F. David
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- Saclay, SPhT
)

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Radiative Decay Sigma+ ---> p gamma in Quantum Chromodynamics

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Conformal Algebra and Multipoint Correlation Functions in Two-Dimensional Statistical Models

V.S. Dotsenko
(
- Nordita
)
,
V.A. Fateev
(
- Landau Inst.
)

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Landau-ginsburg Models With $N=2$ Supersymmetry as Conventional Conformal Theories

A. Marshakov
(
- Lebedev Inst.
)
,
A. Morozov
(
- Moscow, ITEP
)

- Phys.Lett.B 235 (1990) 97-105
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Stress Tensor Correlations and the C Theorem in Models With Exponential Interactions

Marcus T. Grisaru
(
- Brandeis U.
)
,
A. Lerda
(
- MIT, LNS
)
,
S. Penati
(
- Brandeis U.
)
,
D. Zanon
(
- Milan U. and
- INFN, Milan
)

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Irreversibility of the Flux of the Renormalization Group in a 2D Field Theory

A.B. Zamolodchikov
(
- Moscow, ITEP
)

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New selection rules and physical states in 2-D gravity: Conformal gauge

B.H. Lian
(
- Yale U.
)
,
G.J. Zuckerman
(
- Yale U.
)

- Phys.Lett.B 254 (1991) 417-423
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2-D gravity with c = 1 matter

B.H. Lian
(
- Yale U. and
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)
,
G.J. Zuckerman
(
- Yale U. and
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)

- Phys.Lett.B 266 (1991) 21-28
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BRST analysis of physical states for 2-D gravity coupled to c <= 1 matter

Peter Bouwknegt
(
- CERN
)
,
James G. McCarthy
(
- Brandeis U.
)
,
Krzysztof Pilch
(
- Southern California U.
)

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Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory

A.A. Belavin
(
- Landau Inst.
)
,
Alexander M. Polyakov
(
- Landau Inst.
)
,
A.B. Zamolodchikov
(
- CERN and
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)

- Nucl.Phys.B 241 (1984) 333-380,
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•
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On the Structure of the Topological Phase of Two-dimensional Gravity

Edward Witten
(
- Princeton, Inst. Advanced Study
)

- Nucl.Phys.B 340 (1990) 281-332
•
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Two-dimensional gravity and intersection theory on moduli space

Edward Witten
(
- Princeton, Inst. Advanced Study
)

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Mean Field Theory, Topological Field Theory, and Multimatrix Models

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Topological gravity with minimal matter

Keke Li
(
- Caltech
)

- Nucl.Phys.B 354 (1991) 711-724
•
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Topological strings in d < 1

Robbert Dijkgraaf
(
- Princeton U.
)
,
Herman L. Verlinde
(
- Princeton U.
)
,
Erik P. Verlinde
(
- Santa Barbara, KITP
)

- Nucl.Phys.B 352 (1991) 59-86
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Algebraic Geometry and Effective Lagrangians

Emil J. Martinec
(
- Chicago U., EFI and
- Chicago U.
)

- Phys.Lett.B 217 (1989) 431-437
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Catastrophes and the Classification of Conformal Theories

Cumrun Vafa
(
- Harvard U.
)
,
Nicholas P. Warner
(
- MIT
)

- Phys.Lett.B 218 (1989) 51-58
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Calabi-Yau Manifolds and Renormalization Group Flows

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Chiral Rings in N=2 Superconformal Theories

- Nucl.Phys.B 324 (1989) 427-474
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