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 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.

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 CONFORMAL FACTOR AND THE COSMOLOGICAL CONSTANT

1990 ◽  
Vol 05 (19) ◽  
pp. 3811-3829 ◽  
Author(s):  
STEVEN B. GIDDINGS
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
Path Integral ◽  
Conformal Factor ◽  
Positive Cosmological Constant ◽  
Lorentzian Signature ◽  
Wrong Sign ◽  
Euclidean Signature

The issue of the conformal factor in quantum gravity is examined for Lorentzian signature spacetimes. In Euclidean signature, the “wrong” sign of the conformal action makes the path integral undefined, but in Lorentzian signature this sign is tied to the instability of gravity and once this is accounted for the path integral should be well-defined. In this approach it is not obvious that the Baum-Hawking-Coleman mechanism for suppression of the cosmological constant functions. It is conceivable that since the multiuniverse system exhibits an instability for positive cosmological constant, the dynamics should force the system to zero cosmological constant.

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 Liouville theory and matrix models: a Wheeler DeWitt perspective

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
P. Betzios ◽  
O. Papadoulaki
Keyword(s):  
Quantum Gravity ◽  
Path Integral ◽  
Liouville Theory ◽  
Asymptotic Region ◽  
Boundary Theory ◽  
Two Dimensional ◽  
Fermionic Field ◽  
Topology Change ◽  
Single Boundary ◽  
Superspace Description

Abstract We analyse the connections between the Wheeler DeWitt approach for two dimensional quantum gravity and holography, focusing mainly in the case of Liouville theory coupled to c = 1 matter. Our motivation is to understand whether some form of averaging is essential for the boundary theory, if we wish to describe the bulk quantum gravity path integral of this two dimensional example. The analysis hence, is in a spirit similar to the recent studies of Jackiw-Teitelboim (JT)-gravity. Macroscopic loop operators define the asymptotic region on which the holographic boundary dual resides. Matrix quantum mechanics (MQM) and the associated double scaled fermionic field theory on the contrary, is providing an explicit “unitary in superspace” description of the complete dynamics of such two dimensional universes with matter, including the effects of topology change. If we try to associate a Hilbert space to a single boundary dual, it seems that it cannot contain all the information present in the non-perturbative bulk quantum gravity path integral and MQM.

TWO-DIMENSIONAL QUANTUM GRAVITY WITH GENERALIZED ACTION AND COMPACT BOSON

1991 ◽  
Vol 06 (21) ◽  
pp. 1953-1959 ◽  
Author(s):  
I. M. LICHTZIER ◽  
S. D. ODINTSOV
Keyword(s):  
Partition Function ◽  
Quantum Gravity ◽  
Path Integral ◽  
Two Dimensional

The generalized 2-dimensional quantum gravity is considered. The path-integral is evaluated without the need to impose the restrictions on the dimensions of matter. The partition function as well as Hagedorn temperature is also calculated for the case when one boson is compact.

scholarly journals Schwarzian quantum mechanics as a Drinfeld-Sokolov reduction of BF theory

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Fridrich Valach ◽  
Donald R. Youmans
Keyword(s):  
Quantum Mechanics ◽  
Partition Function ◽  
Gauge Group ◽  
Path Integral ◽  
Coadjoint Orbits ◽  
Two Dimensional ◽  
Edge States ◽  
Class Constraint ◽  
Action Functional ◽  
Bf Theory

Abstract We give an interpretation of the holographic correspondence between two-dimensional BF theory on the punctured disk with gauge group PSL(2, ℝ) and Schwarzian quantum mechanics in terms of a Drinfeld-Sokolov reduction. The latter, in turn, is equivalent to the presence of certain edge states imposing a first class constraint on the model. The constrained path integral localizes over exceptional Virasoro coadjoint orbits. The reduced theory is governed by the Schwarzian action functional generating a Hamiltonian S1-action on the orbits. The partition function is given by a sum over topological sectors (corresponding to the exceptional orbits), each of which is computed by a formal Duistermaat-Heckman integral.

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.

The partition function of two-dimensional quantum gravity

1989 ◽  
Vol 233 (1-2) ◽  
pp. 79-84 ◽  
Author(s):  
M.A. Awada ◽  
A.H. Chamseddine
Keyword(s):  
Partition Function ◽  
Quantum Gravity ◽  
Two Dimensional
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