A Continuum Approach to 2D-Quantum Gravity for c>1

1997 ◽  
Vol 11 (26n27) ◽  
pp. 3247-3279
Author(s):  
M. Martellini ◽  
M. Spreafico ◽  
K. Yoshida
Keyword(s):  
Quantum Gravity ◽  
Scalar Curvature ◽  
Free Parameter ◽  
Central Charge ◽  
Flat Space ◽  
String Tension ◽  
Physical Significance ◽  
Two Dimensional ◽  
Continuum Approach ◽  
Gauge Fixing

Two dimensional induced quantum gravity with matter central charge c>1 is studied by carefully treating both diffeomorphism and Weyl symmetries. It is shown that, for the gauge fixing condition R(g) (scalar curvature) = const, one obtains a modification of the David–Distler–Kawai version of KPZ scaling. We obtain a class of models with real string tension for all values c>1. They contain a free parameter which is, however, strongly constrained by the requirement of the non triviality of the model. The possible physical significance of the new model is discussed. In particular we note that it describes smooth surfaces imbedded in d-dimensional flat space time for arbitrary d, which is consistent with recent numerical results for d=3.

scholarly journals The two-sphere partition function in two-dimensional quantum gravity

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Dionysios Anninos ◽  
Teresa Bautista ◽  
Beatrix Mühlmann
Keyword(s):  
Partition Function ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Path Integral ◽  
Central Charge ◽  
Liouville Theory ◽  
Two Dimensional ◽  
Positive Cosmological Constant ◽  
Gauge Fixing ◽  
Semiclassical Expansion

Abstract We study the Euclidean path integral of two-dimensional quantum gravity with positive cosmological constant coupled to conformal matter with large and positive central charge. The problem is considered in a semiclassical expansion about a round two-sphere saddle. We work in the Weyl gauge whereby the computation reduces to that for a (timelike) Liouville theory. We present results up to two-loops, including a discussion of contributions stemming from the gauge fixing procedure. We exhibit cancelations of ultraviolet divergences and provide a path integral computation of the central charge for timelike Liouville theory. Combining our analysis with insights from the DOZZ formula we are led to a proposal for an all orders result for the two-dimensional gravitational partition function on the two-sphere.

scholarly journals A GENERALIZED MODEL FOR TWO-DIMENSIONAL QUANTUM GRAVITY AND DYNAMICS OF RANDOM SURFACES FOR d>1

1994 ◽  
Vol 09 (22) ◽  
pp. 2009-2018 ◽  
Author(s):  
M. MARTELLINI ◽  
M. SPREAFICO ◽  
K. YOSHIDA
Keyword(s):  
Quantum Gravity ◽  
Effective Field Theory ◽  
Continuum Model ◽  
Central Charge ◽  
Flat Space ◽  
Effective Field ◽  
Two Dimensional ◽  
Large Area ◽  
Random Surfaces ◽  
Area Expansion

The possible interpretations of a new continuum model for the two-dimensional quantum gravity for d>1 (d=matter central charge), obtained by carefully treating both diffeomorphism and Weyl symmetries, are discussed. In particular we note that an effective field theory is achieved in low energy (large area) expansion, that may represent smooth self-avoiding random surfaces embedded in a d-dimensional flat space-time for arbitrary d. Moreover the values of some critical exponents are computed, that are in agreement with some recent numerical results.

THE APPEARANCE OF MATTER FIELDS FROM QUANTUM FLUCTUATIONS OF 2D-GRAVITY

1989 ◽  
Vol 04 (22) ◽  
pp. 2125-2139 ◽  
Author(s):  
V.A. KAZAKOV
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
Critical Exponent ◽  
2D Gravity ◽  
Central Charge ◽  
Quantum Fluctuations ◽  
Two Dimensional ◽  
Conformal Fields ◽  
Exactly Solvable ◽  
Matter Fields

It is established that various critical regimes may occur for a model of two-dimensional pure quantum gravity. These regimes correspond to the presence of effective fields with scaling dimensions Δk=−γ str ·k/2, k=1, 2, 3 ..., where γ str =−1/m, m=2, 3, 4 ... is the critical exponent of “string susceptibility” (with respect to the cosmological constant). This behaviour is typical for unitary conformal fields with the central charge c=1−6/m(m+1) in the presence of 2D-quantum gravity. We use the framework of loop equations for the invariant boundary functional, which are exactly solvable in this case.

THE METHOD OF COADJOINT ORBITS: AN ALGORITHM FOR THE CONSTRUCTION OF INVARIANT ACTIONS

1990 ◽  
Vol 05 (20) ◽  
pp. 3943-3983 ◽  
Author(s):  
GUSTAV W. DELIUS ◽  
PETER VAN NIEUWENHUIZEN ◽  
V. G. J. RODGERS
Keyword(s):  
Quantum Gravity ◽  
Central Extension ◽  
Central Charge ◽  
Virasoro Algebra ◽  
Coadjoint Orbit ◽  
The Other ◽  
Coadjoint Orbits ◽  
Two Dimensional ◽  
Supersymmetric Extension ◽  
Infinite Dimensional

The method of coadjoint orbits produces for any infinite dimensional Lie (super) algebra A with nontrivial central charge an action for scalar (super) fields which has at least the symmetry A. In this article, we try to make this method accessible to a larger audience by analyzing several examples in more detail than in the literature. After working through the Kac-Moody and Virasoro cases, we apply the method to the super Virasoro algebra and reobtain the supersymmetric extension of Polyakov's local nonpolynomial action for two-dimensional quantum gravity. As in the Virasoro case this action corresponds to the coadjoint orbit of a pure central extension. We further consider the actions corresponding to the other orbits of the super Virasoro algebra. As a new result we construct the actions for the N = 2 super Virasoro algebra.

scholarly journals MINBU Distribution of Two-Dimensional Quantum Gravity: Simulation Result and Semiclassical Analysis

1997 ◽  
Vol 12 (04) ◽  
pp. 757-780 ◽  
Author(s):  
S. Ichinose ◽  
N. Tsuda ◽  
T. Yukawa
Keyword(s):  
Quantum Gravity ◽  
Central Charge ◽  
Surface Topology ◽  
Two Dimensional ◽  
Semiclassical Analysis ◽  
Semiclassical Approach ◽  
Infrared Regularization ◽  
Derivative Term ◽  
Total Derivative Term ◽  
Baby Universe

We analyze the MINBU distribution of two-dimensional quantum gravity. New data of R2-gravity by the Monte Carlo simulation and its theoretical analysis by the semiclassical approach are presented. In the distribution, the cross-over phenomenon takes place at some size of the baby universe where the randomness competes with the smoothing (or roughening) force of R2-term. The dependence on the central charge cm and on the R2-coupling are explained for R2-gravity, which includes the ordinary 2d quantum gravity. The R2-Liouville solution plays the central role in the semiclassical analysis. A total derivative term (surface term) and the infrared regularization play important roles. The surface topology is that of a sphere.

scholarly journals The two-sphere partition function in two-dimensional quantum gravity at fixed area

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Beatrix Mühlmann
Keyword(s):  
Partition Function ◽  
Quantum Gravity ◽  
Path Integral ◽  
Central Charge ◽  
Gravity Theory ◽  
Feynman Diagrams ◽  
Two Dimensional ◽  
Loop Order ◽  
Fixed Area

Abstract We discuss two-dimensional quantum gravity coupled to conformal matter and fixed area in a semiclassical large and negative matter central charge limit. In this setup the gravity theory — otherwise highly fluctuating — admits a round two-sphere saddle. We discuss the two-sphere partition function up to two-loop order from the path integral perspective. This amounts to studying Feynman diagrams incorporating the fixed area constraint on the round two-sphere. In particular we find that all ultraviolet divergences cancel to this order. We compare our results with the two-sphere partition function obtained from the DOZZ formula.

COVARIANT OPERATOR FORMALISM OF TWO-DIMENSIONAL TOPOLOGICAL GRAVITY

1992 ◽  
Vol 07 (13) ◽  
pp. 3105-3131
Author(s):  
NORIAKI IKEDA
Keyword(s):  
Quantum Gravity ◽  
Two Dimensional ◽  
Operator Formalism ◽  
Canonical Operator ◽  
Covariant Operator ◽  
Gauge Fixing ◽  
Topological Gravity

The manifestly covariant canonical operator formalism of two-dimensional topological gravity is formulated. Its unitarity is confirmed by means of constructing the Kugo–Ojima's quartets. A number of new symmetries are found by adopting a particular gauge fixing condition. These symmetries correspond to the "choral symmetry" generated by the 4N-dimensional Poincaré-like superalgebra in the ordinary N-dimensional quantum gravity.

scholarly journals A CONTINUUM STRING MODEL FOR D>1

1992 ◽  
Vol 07 (18) ◽  
pp. 1667-1677 ◽  
Author(s):  
M. MARTELLINI ◽  
M. SPREAFICO ◽  
K. YOSHIDA
Keyword(s):  
Classical Result ◽  
2D Gravity ◽  
Central Charge ◽  
String Model ◽  
String Tension ◽  
The Real ◽  
Gauge Fixing ◽  
Weyl Symmetry ◽  
Taking Care

The non-critical string (2D gravity coupled to the matter with central charge D) is quantized by taking care of both diffeomorphism and Weyl symmetries. In incorporating the gauge fixing with respect to the Weyl symmetry, through the condition Rg=const., one modifies the classical result of Distler and Kawai. In particular one obtains the real string tension for an arbitrary value of central charge D.

scholarly journals ON THE EXACT OPERATOR FORMALISM OF TWO-DIMENSIONAL LIOUVILLE QUANTUM GRAVITY IN MINKOWSKI SPACE-TIME

1994 ◽  
Vol 09 (05) ◽  
pp. 667-710 ◽  
Author(s):  
YOICHI KAZAMA ◽  
HERMANN NICOLAI
Keyword(s):  
Quantum Gravity ◽  
Minkowski Space ◽  
Central Charge ◽  
Free Field ◽  
Space Time ◽  
Cosmological Term ◽  
Two Dimensional ◽  
Operator Formalism ◽  
Minkowski Space Time ◽  
Exponential Operator

A detailed re-examination is made of the exact operator formalism of two-dimensional Liouville quantum gravity in Minkowski space-time with the cosmological term fully taken into account. Making use of the canonical mapping from the interacting Liouville field into a free field, we focus on the problem of how the Liouville exponential operator should be properly defined. In particular, the condition of mutual locality among the exponential operators is carefully analyzed, and a new solution, which is neither smoothly connected nor relatively local to the existing solution, is found. Our analysis indicates that, in Minkowski space-time, coupling gravity to matter with central charge d<1 is problematical. For d=1, our new solution appears to be the appropriate one; for this value of d, we demonstrate that the operator equation of motion is satisfied to all orders in the cosmological constant with a certain regularization. As an application of the formalism, an attempt is made to study how the basic generators of the ground ring get modified due to the inclusion of the cosmological term. Our investigation, although incomplete, suggests that in terms of the canonically mapped free field the ground ring is not modified.

UNITARY THEORY OF TWO-DIMENSIONAL QUANTUM GRAVITY AND ITS EXACT COVARIANT OPERATOR SOLUTION

1991 ◽  
Vol 06 (22) ◽  
pp. 3955-3971 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Quantum Gravity ◽  
Two Dimensional ◽  
Operator Formalism ◽  
Unitary Theory ◽  
Operator Solution ◽  
Canonical Operator ◽  
Weyl Invariance ◽  
Covariant Operator ◽  
Gauge Fixing

The manifestly covariant canonical operator formalism of two-dimensional quantum gravity is formulated on the basis of Sato’s gauge-fixing of the Weyl invariance. The unitarity problem, due to ghost-counting mismatch, is resolved by making the gravitational FP ghosts also play the role of the Weyl FP ghosts. All two-dimensional (anti)commutators between fundamental fields are explicitly obtained.

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