PROPERTIES OF LOOP EQUATIONS FOR THE HERMITIAN MATRIX MODEL AND FOR TWO-DIMENSIONAL QUANTUM GRAVITY

1990 ◽  
Vol 05 (22) ◽  
pp. 1753-1763 ◽  
Author(s):  
J. AMBJØRN ◽  
YU. M. MAKEENKO
Keyword(s):  
Quantum Gravity ◽  
Matrix Model ◽  
Hermitian Matrix ◽  
General Procedure ◽  
Iterative Solution ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Continuum Equation ◽  
Hermitian Matrix Model ◽  
The Continuum

We study the properties of the loop equations for the N × N Hermitian matrix model with arbitrary (even) interaction as well as of their continuum limit, associated with the two-dimensional quantum gravity. We apply the general procedure of iterative solution proposed recently by David. We relate the specific heat to the singular behavior of the connected correlator of two loops. We solve the continuum equation to a few lower orders in the string coupling constant, obtaining results for macroscopic loops including the case of a multicritical fixed point.

scholarly journals Langevin Simulation of a Bottomless Hermitian Matrix Model for Two Dimensional Quantum Gravity

1994 ◽  
Vol 91 (3) ◽  
pp. 599-610 ◽  
Author(s):  
M. Kanenaga ◽  
M. Mizutani ◽  
M. Namiki ◽  
I. Ohba ◽  
S. Tanaka
Keyword(s):  
Quantum Gravity ◽  
Matrix Model ◽  
Hermitian Matrix ◽  
Two Dimensional ◽  
Langevin Simulation ◽  
Hermitian Matrix Model

MATHEMATICAL ASPECTS OF THE NON-PERTURBATIVE 2D QUANTUM GRAVITY

1990 ◽  
Vol 05 (25) ◽  
pp. 2079-2083 ◽  
Author(s):  
A. R. ITS ◽  
A. V. KITAEV
Keyword(s):  
Quantum Gravity ◽  
Matrix Model ◽  
Hermitian Matrix ◽  
Continuous Limit ◽  
Hermitian Matrix Model

We present rigorous mathematical results for the continuous limit for the hermitian matrix model in connection with the non-perturbative theory of 2D quantum gravity.

TENSOR MODEL FOR GRAVITY AND ORIENTABILITY OF MANIFOLD

1991 ◽  
Vol 06 (28) ◽  
pp. 2613-2623 ◽  
Author(s):  
NAOKI SASAKURA
Keyword(s):  
Quantum Gravity ◽  
Hermitian Matrix ◽  
Three Dimensional ◽  
Tensor Model ◽  
Two Dimensional ◽  
Tensor Models ◽  
Arbitrary Dimensions ◽  
Dynamical Triangulation ◽  
Hermitian Matrix Model ◽  
Special Case

We investigate the relation between rank-three tensor models and the dynamical triangulation model of three-dimensional quantum gravity, and discuss the orientability of the manifold and the corresponding tensor models. We generalize the orientable tensor models to arbitrary dimensions, which include the two-dimensional Hermitian matrix model as a special case.

FERMIONS IN THE TOPOLOGICAL EXPANSION OF MATRIX MODELS

1991 ◽  
Vol 06 (09) ◽  
pp. 781-787
Author(s):  
G. FERRETTI
Keyword(s):  
Free Energy ◽  
Matrix Models ◽  
Matrix Model ◽  
Hermitian Matrix ◽  
Coupling Constant ◽  
Counting Problem ◽  
Planar Limit ◽  
Quartic Interaction ◽  
Hermitian Matrix Model ◽  
Topological Expansion

The hermitian matrix model with quartic interaction is studied in presence of fermionic variables. We obtain the contribution to the free energy due to the presence of fermions. The first two terms beyond the planar limit are explicitly found for all values of the coupling constant g. These terms represent the solution of the counting problem for vacuum diagrams with one or two fermionic loops.

scholarly journals Genus expansion of matrix models and ћ expansion of KP hierarchy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
A. Andreev ◽  
A. Popolitov ◽  
A. Sleptsov ◽  
A. Zhabin
Keyword(s):  
Matrix Models ◽  
Matrix Model ◽  
Special Interest ◽  
Hermitian Matrix ◽  
Geometric Meaning ◽  
Kp Hierarchy ◽  
Hurwitz Numbers ◽  
Kp Equations ◽  
Genus Expansion ◽  
Hermitian Matrix Model

Abstract We study ћ expansion of the KP hierarchy following Takasaki-Takebe [1] considering several examples of matrix model τ-functions with natural genus expansion. Among the examples there are solutions of KP equations of special interest, such as generating function for simple Hurwitz numbers, Hermitian matrix model, Kontsevich model and Brezin-Gross-Witten model. We show that all these models with parameter ћ are τ-functions of the ћ-KP hierarchy and the expansion in ћ for the ћ-KP coincides with the genus expansion for these models. Furthermore, we show a connection of recent papers considering the ћ-formulation of the KP hierarchy [2, 3] with original Takasaki-Takebe approach. We find that in this approach the recovery of enumerative geometric meaning of τ-functions is straightforward and algorithmic.

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.

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.

scholarly journals QUANTUM RINGS AND RECURSION RELATIONS IN 2D QUANTUM GRAVITY

1992 ◽  
Vol 07 (16) ◽  
pp. 1419-1425 ◽  
Author(s):  
SHAMIT KACHRU
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Quantum Gravity ◽  
Matrix Model ◽  
Ring Structure ◽  
Two Dimensional ◽  
Recursion Relations ◽  
Quantum Rings ◽  
Bulk Scattering

I study tachyon condensate perturbations to the action of the two-dimensional string theory corresponding to the c=1 matrix model. These are shown to deform the action of the ground ring on the tachyon modules, confirming a conjecture of Witten. The ground ring structure is used to derive recursion relations which relate (N+1) and N tachyon bulk scattering amplitudes. These recursion relations allow one to compute all bulk amplitudes.

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