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.

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.

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

scholarly journals HIGHER DERIVATIVE QUANTUM GRAVITY WITH TORSION IN THE CONFORMALLY SELF-DUAL LIMIT

1993 ◽  
Vol 02 (01) ◽  
pp. 51-58 ◽  
Author(s):  
E. ELIZALDE ◽  
S.D. ODINTSOV
Keyword(s):  
Quantum Gravity ◽  
Path Integral ◽  
Scaling Law ◽  
Two Dimensional ◽  
Fixed Volume ◽  
Higher Derivative

The path integral for higher-derivative quantum gravity with torsion is considered. Applying the methods of two-dimensional quantum gravity, this path integral is analyzed in the limit of conformally self-dual metrics. A scaling law for fixed-volume geometry is obtained.

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.

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.

CONTINUUM SCHWINGER-DYSON EQUATIONS AND UNIVERSAL STRUCTURES IN TWO-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (08) ◽  
pp. 1385-1406 ◽  
Author(s):  
MASAFUMI FUKUMA ◽  
HIKARU KAWAI ◽  
RYUICHI NAKAYAMA
Keyword(s):  
Partition Function ◽  
Quantum Gravity ◽  
Matrix Models ◽  
Square Root ◽  
Two Dimensional ◽  
Kp Hierarchy ◽  
Kdv Hierarchy ◽  
The One ◽  
Matter Fields ◽  
The Continuum

We study the continuum Schwinger-Dyson equations for nonperturbative two-dimensional quantum gravity coupled to various matter fields. The continuum Schwinger-Dyson equations for the one-matrix model are explicitly derived and turn out to be a formal Virasoro condition on the square root of the partition function, which is conjectured to be the τ function of the KdV hierarchy. Furthermore, we argue that general multi-matrix models are related to the W algebras and suitable reductions of KP hierarchy and its generalizations.

Sign in / Sign up

Export Citation Format

Share Document