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.

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.

TWO-DIMENSIONAL QUANTUM GRAVITY, MATRIX MODELS AND STRING THEORY

1993 ◽  
Vol 08 (07) ◽  
pp. 1185-1244 ◽  
Author(s):  
KREŠIMIR DEMETERFI
Keyword(s):  
String Theory ◽  
Quantum Gravity ◽  
Matrix Models ◽  
Lattice Models ◽  
Field Method ◽  
Two Dimensional ◽  
Large N ◽  
The One ◽  
Low Dimensional ◽  
Lattice Approach

We review some results of the recent progress in understanding two-dimensional quantum gravity and low-dimensional string theories based on the lattice approach. The possibility to solve the lattice models exactly comes from their equivalence to large N matrix models. We describe various matrix models and their continuum limits, and discuss in some detail the phase structure of Hermitian one-matrix models. For the one-dimensional matrix model we discuss its field theoretic formulation through a collective field method and summarize some perturbative results. We compare the results obtained from matrix models to the results in the continuum approach to string theory.

STABILIZED MATRIX MODELS FOR NONPERTURBATIVE TWO-DIMENSIONAL QUANTUM GRAVITY

1994 ◽  
Vol 09 (21) ◽  
pp. 3751-3771 ◽  
Author(s):  
JOSHUA FEINBERG
Keyword(s):  
Nonperturbative Effects ◽  
Quantum Gravity ◽  
Matrix Models ◽  
Two Dimensional ◽  
Hartree Fock ◽  
Kdv Hierarchy ◽  
Multicritical Points ◽  
Dimensional Gravity ◽  
Arbitrary Weight ◽  
Genus Expansion

A thorough analysis of stochastically stabilized Hermitian one-matrix models for two-dimensional quantum gravity at all its (2, 2k − 1) multicritical points is made. It is stressed that only the zero fermion sector of the supersymmetric Hamiltonian, i.e. the forward Fokker–Planck Hamiltonian, is relevant for the analysis of bosonic matter coupled to two-dimensional gravity. Therefore, supersymmetry breaking is not the physical mechanism that creates nonperturbative effects in the case of points of even multicriticality k. Nonperturbative effects in the string coupling constant g str result in a loss of any explicit relation to the KdV hierarchy equations in the latter case, while maintaining the perturbative genus expansion. As a by-product of our analysis it is explicitly proved that polynomials orthogonal relative to an arbitrary weight exp (−βV (x)) along the whole real line obey a Hartree–Fock equation.

scholarly journals Multiple phases in a generalized Gross-Witten-Wadia matrix model

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Jorge G. Russo ◽  
Miguel Tierz
Keyword(s):  
Partition Function ◽  
Matrix Models ◽  
Characteristic Polynomial ◽  
Matrix Model ◽  
Phase Structure ◽  
Unitary Matrix ◽  
Two Dimensional ◽  
Toeplitz Determinants ◽  
Dimensional Parameter ◽  
Planar Limit

Abstract We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed Cauchy ensemble. Exact formulas for the partition function and Wilson loops are given in terms of Toeplitz determinants and minors and large N results are obtained by using Szegö theorem with a Fisher-Hartwig singularity. In the large N (planar) limit with two scaled couplings, the theory exhibits a surprisingly intricate phase structure in the two-dimensional parameter space.

scholarly journals Quantum gravity as a multitrace matrix model

2017 ◽  
Vol 32 (31) ◽  
pp. 1750180
Author(s):  
Badis Ydri ◽  
Cherine Soudani ◽  
Ahlam Rouag
Keyword(s):  
Quantum Gravity ◽  
Matrix Models ◽  
Large Class ◽  
Matrix Model ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Topology Change ◽  
New Model ◽  
And Topology ◽  
Emergent Geometry

We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of two-dimensional quantum gravity which works away from two dimensions and captures a large class of spaces admitting a finite spectral triple. These multitrace matrix models sustain emergent geometry as well as growing dimensions and topology change.

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 SUPERLOOP EQUATIONS AND TWO-DIMENSIONAL SUPERGRAVITY

1992 ◽  
Vol 07 (21) ◽  
pp. 5337-5367 ◽  
Author(s):  
L. ALVAREZ-GAUMÉ ◽  
H. ITOYAMA ◽  
J.L. MAÑES ◽  
A. ZADRA
Keyword(s):  
Partition Function ◽  
Discrete Model ◽  
Continuum Limit ◽  
Basic Assumption ◽  
Scaling Limit ◽  
Integrable Hierarchy ◽  
Two Dimensional ◽  
Virasoro Constraints ◽  
Double Scaling Limit ◽  
The Continuum

We propose a discrete model whose continuum limit reproduces the string susceptibility and the scaling dimensions of (2, 4m) minimal superconformal models coupled to 2D supergravity. The basic assumption in our presentation is a set of super-Virasoro constraints imposed on the partition function. We recover the Neveu-Schwarz and Ramond sectors of the theory, and we are also able to evaluate all planar loop correlation functions in the continuum limit. We find evidence to identify the integrable hierarchy of nonlinear equations describing the double scaling limit as a supersymmetric generalization of KP studied by Rabin.

The Effect of Insulated Cracks on Heat Transfer of Thermoelectric Plates Using Peridynamics

2020 ◽  
Vol 10 (4) ◽  
pp. 25-39
Author(s):  
Migbar Assefa Zeleke ◽  
Lai Xin ◽  
Liu Lisheng
Keyword(s):  
Electric Fields ◽  
Crack Surface ◽  
Temperature Fields ◽  
Two Dimensional ◽  
Electrical Potentials ◽  
Non Local ◽  
The One ◽  
Growing Cracks ◽  
Good Agreement ◽  
The Continuum

In this article, peridynamic (PD) theory is applied to analyze two-dimensional heat conduction of thermoelectric plate with discontinuities. It is a well-known fact that heat flux is undefined at the crack tip and causes the temperature field across the crack surface discontinuous. Hence, numerical procedures like finite element method (FEM) became unsuccessful to capture details of moving discontinuities like growing cracks. Therefore, this article proposes a PD theory that is appropriate in resolving moving discontinuities in thermal and electric fields. The PD equations were constructed by writing the continuum-based electrical potentials and temperature fields in the form of their respective non-local integrals that are remarkably powerful in solving continuum problems whether the authors have moving discontinuities or not. To elucidate the trustworthiness of the PD theory, the results in the case of stationary cracks are compared with the one from FEM and witnessed that they were in good agreement.

scholarly journals Large Quantum Gravity Effects: Backreaction on Matter

1997 ◽  
Vol 12 (32) ◽  
pp. 2407-2413 ◽  
Author(s):  
Rodolfo Gambini ◽  
Jorge Pullin
Keyword(s):  
Quantum Gravity ◽  
Coherent States ◽  
Rapid Loss ◽  
Gravity Effects ◽  
Dimensional Gravity ◽  
The One ◽  
Loss Of Coherence ◽  
Matter Sector ◽  
Matter Fields ◽  
Large Quantum

We re-examine the large quantum gravity effects discovered by Ashtekar in the context of (2+1)-dimensional gravity coupled to matter. We study an alternative one-parameter family of coherent states of the theory in which the large quantum gravity effects on the metric can be diminished, at the expense of losing coherence in the matter sector. Which set of states is the one that occurs in nature will determine if the large quantum gravity effects are actually observable as wild fluctuations of the metric or rapid loss of coherence of matter fields.

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