scholarly journals Matrix models and deformations of JT gravity

2020 ◽  
Vol 476 (2244) ◽  
pp. 20200582
Author(s):  
Edward Witten
Keyword(s):  
Matrix Models ◽  
Path Integral ◽  
Matrix Model ◽  
Quantum Systems ◽  
Quantum Mechanical ◽  
Two Dimensional ◽  
Quantum Mechanical System ◽  
Specific Procedure ◽  
Dimensional Theory ◽  
Specific Quantum

Recently, it has been found that Jackiw-Teitelboim (JT) gravity, which is a two-dimensional theory with bulk action − 1 / 2 ∫ d 2 x g ϕ ( R + 2 ) , is dual to a matrix model, that is, a random ensemble of quantum systems rather than a specific quantum mechanical system. In this article, we argue that a deformation of JT gravity with bulk action − 1 / 2 ∫ d 2 x g ( ϕ R + W ( ϕ ) ) is likewise dual to a matrix model. With a specific procedure for defining the path integral of the theory, we determine the density of eigenvalues of the dual matrix model. There is a simple answer if W (0) = 0, and otherwise a rather complicated answer.

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.

scholarly journals The path integral of 3D gravity near extremality; or, JT gravity with defects as a matrix integral

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Henry Maxfield ◽  
Gustavo J. Turiaci
Keyword(s):  
Classical Solution ◽  
Path Integral ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Matrix Integral ◽  
Pure Gravity ◽  
Extremal Limit ◽  
3D Gravity

Abstract We propose that a class of new topologies, for which there is no classical solution, should be included in the path integral of three-dimensional pure gravity, and that their inclusion solves pathological negativities in the spectrum, replacing them with a nonperturbative shift of the BTZ extremality bound. We argue that a two dimensional calculation using a dimensionally reduced theory captures the leading effects in the near extremal limit. To make this argument, we study a closely related two-dimensional theory of Jackiw-Teitelboim gravity with dynamical defects. We show that this theory is equivalent to a matrix integral.

scholarly journals PERTURBATIVE VACUA FROM IIB MATRIX MODEL

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2279-2280
Author(s):  
HIKARU KAWAI ◽  
MATSUO SATO
Keyword(s):  
String Theory ◽  
Path Integral ◽  
Matrix Model ◽  
Moduli Space ◽  
Two Dimensional ◽  
Reduced Models ◽  
Yang Mills ◽  
Large N ◽  
Super Yang Mills Theory

It has not been clarified whether a matrix model can describe various vacua of string theory. In this talk, we show that the IIB matrix model includes type IIA string theory1. In the naive large N limit of the IIB matrix model, configurations consisting of simultaneously diagonalizable matrices form a moduli space, although the unique vacuum would be determined by complicated dynamics. This moduli space should correspond to a part of perturbatively stable vacua of string theory. Actually, one point on the moduli space represents type IIA string theory. Instead of integrating over the moduli space in the path-integral, we can consider each of the simultaneously diagonalizable configurations as a background and set the fluctuations of the diagonal elements to zero. Such procedure is known as quenching in the context of the large N reduced models. By quenching the diagonal elements of the matrices to an appropriate configuration, we show that the quenched IIB matrix model is equivalent to the two-dimensional large N [Formula: see text] super Yang-Mills theory on a cylinder. This theory is nothing but matrix string theory and is known to be equivalent to type IIA string theory. As a result, we find the manner to take the large N limit in the IIB matrix model.

scholarly journals MATRIX MODELS AND NON-PERTURBATIVE STRING PROPAGATION IN TWO-DIMENSIONAL BLACK HOLE BACKGROUNDS

1993 ◽  
Vol 08 (14) ◽  
pp. 1331-1341 ◽  
Author(s):  
SUMIT R. DAS
Keyword(s):  
Black Hole ◽  
Wave Function ◽  
String Theory ◽  
Matrix Models ◽  
Matrix Model ◽  
Asymptotic Region ◽  
Two Dimensional ◽  
White Hole ◽  
Dimensional Black Hole ◽  
String Propagation

We identify a quantity in the c = 1 matrix model which describes the wave function for physical scattering of a tachyon from a black hole of the two-dimensional critical string theory. At the semiclassical level this quantity corresponds to the usual picture of a wave coming in from infinity, part of which enters the black hole becoming singular at the singularity, while the rest is scattered back to infinity, with nothing emerging from the white hole. We find, however, that the exact non-perturbative wave function is non-singular at the singularity and appears to end up in the asymptotic region "behind" the singularity.

scholarly journals Boundary dynamics and topology change in quantum mechanics

2015 ◽  
Vol 12 (08) ◽  
pp. 1560011 ◽  
Author(s):  
J. M. Pérez-Pardo ◽  
M. Barbero-Liñán ◽  
A. Ibort
Keyword(s):  
Boundary Conditions ◽  
Differential Operators ◽  
Necessary Conditions ◽  
Quantum Systems ◽  
Quantum Mechanical ◽  
Manifolds With Boundary ◽  
Quantum Mechanical System ◽  
Topology Change ◽  
And Topology ◽  
Boundary Dynamics

We show how to use boundary conditions to drive the evolution on a quantum mechanical system. We will see how this problem can be expressed in terms of a time-dependent Schrödinger equation. In particular, we will need the theory of self-adjoint extensions of differential operators in manifolds with boundary. An introduction of the latter as well as meaningful examples will be given. It is known that different boundary conditions can be used to describe different topologies of the associated quantum systems. We will use the previous results to study the topology change and to obtain necessary conditions to accomplish it in a dynamical way.

Time-dependence and holography in the c=1 matrix model This paper was presented at the Theory CANADA 4 conference, held at Centre de recherches mathématiques, Montréal, Québec, Canada on 4–7 June 2008.

2009 ◽  
Vol 87 (3) ◽  
pp. 263-266
Author(s):  
Joanna L. Karczmarek
Keyword(s):  
String Theory ◽  
Time Dependence ◽  
Matrix Model ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Two Dimensional ◽  
The Matrix ◽  
Background Material ◽  
The Relationship ◽  
Time Dependent Solution

Ideas related to the study of time-dependence in two dimensional Liouville string theory using the c=1 matrix model are reviewed. Following an introduction to Liouville string theory, the matrix model and the relationship between the two, an example of an exact quantum mechanical time-dependent solution is given. There is a brief discussion of the holographic issues complicating the construction of the exact spacetime interpretation of such solutions. An attempt is made to include sufficient background material to make the presentation self-contained and accessible to a non-expert.

MATRIX MODELS AND BLACK HOLES

1993 ◽  
Vol 08 (01) ◽  
pp. 69-78 ◽  
Author(s):  
SUMIT R. DAS
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
String Theory ◽  
Matrix Models ◽  
Matrix Model ◽  
Integral Transform ◽  
Two Dimensional ◽  
Black Hole Background

We show that an integral transform of the fluctuations of the collective field of the d=1 matrix model satisfy the same linearized equation as that of the massless “tachyon” in the black hole background of the two-dimensional critical string. This suggests that the d=1 matrix model may provide a non-perturbative description of black holes in two-dimensional string theory.

scholarly journals QUANTIZATION AND THE ISSUE OF TIME FOR VARIOUS TWO-DIMENSIONAL MODELS OF GRAVITY

1994 ◽  
Vol 03 (01) ◽  
pp. 281-284 ◽  
Author(s):  
THOMAS STROBL
Keyword(s):  
Time Dependent ◽  
Quantum Mechanical ◽  
Two Dimensional ◽  
Momentum Representation ◽  
Quantum Mechanical System ◽  
Liouville Gravity ◽  
Finite Dimensional ◽  
Constraint Algebra ◽  
Models Of Gravity ◽  
Dirac Constraints

It is shown that the models of 2D Liouville Gravity, 2D Black Hole- and R2-Gravity are embedded in the Katanaev-Volovich model of 2D NonEinsteinian Gravity. Different approaches to the formulation of a quantum theory for the above systems are then presented: The Dirac constraints can be solved exactly in the momentum representation, the path integral can be integrated out, and the constraint algebra can be explicitely canonically abelianized, thus allowing also for a (superficial) reduced phase space quantization. Non-trivial dynamics are obtained by means of time dependent gauges. All of these approaches lead to the same finite dimensional quantum mechanical system.

scholarly journals ACTION WITH ACCELERATION I: EUCLIDEAN HAMILTONIAN AND PATH INTEGRAL

2013 ◽  
Vol 28 (27) ◽  
pp. 1350137 ◽  
Author(s):  
BELAL E. BAAQUIE
Keyword(s):  
Boundary Conditions ◽  
Path Integral ◽  
Degrees Of Freedom ◽  
Similarity Transformation ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Quantum Mechanical System ◽  
The Matrix ◽  
Correct Boundary Conditions ◽  
Acceleration Term

An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the acceleration Lagrangian and the path integral with the correct boundary conditions. Due to the acceleration term, the state space depends on both position and velocity — and hence the Euclidean Hamiltonian depends on two degrees of freedom. The Hamiltonian for the acceleration system is non-Hermitian and can be mapped to a Hermitian Hamiltonian using a similarity transformation; the matrix elements of the similarity transformation are explicitly evaluated.

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