# Badis Ydri

Badis Ydri

Professor

Lattice Quantum Mechanics and Matrix Quantum Gravity

## About

194

Publications

48,386

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1,044

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Introduction

Quantum Gravity

**Skills and Expertise**

## Publications

Publications (194)

We construct noncommutative Euclidean/Lorentzian ${\bf AdS}^2_{\theta}$ black holes and their Yang-Mills matrix models.
It is shown that black hole evaporation presents itself as an inverse emergent gravity phase transition in a path integral formulation and thus the whole process is unitary and there is no information loss problem.
This result i...

Quantum mechanics in which the degrees of freedom are matrices is known to admit, under certain conditions such as those found in the case of the celebrated BFSS/BMN model, a gravitational dual.
This matrix quantum mechanics or mQM is characterized by gauge symmetry and supersymmetry.
Lattice mQM is the study of mQM on a lattice (discretized time)....

The correspondence between quantum mechanics and noncommutative geometry is illustrated in the context of the noncommutative ${\rm AdS}^2_{\theta}/{\rm CFT_1}$ duality where ${\rm CFT}_1$ is identified as conformal quantum mechanics. This model is conjectured to describe the gauge/gravity correspondence in one dimension. Applications to quantum bla...

A complete course on the theory of general relativity and its differential geometry.

In this thesis, we studied a Gaussian approximation to the bosonic part of the BFSS matrix model using Monte Carlo simulations based on the Metropolis algorithm. We reproduce with great accuracy the stringy Hagedorn phase transition from a confinement (black string) phase to a deconfinement (black hole) phase. We used the Polyakov loop as an order...

The Wilsonian renormalization group approach to matrix models is outlined and applied to multitrace matrix models with an emphasis on the computation of the fixed points which could describe the phase structure of noncommutative scalar phi-four theory.

In this paper, we present the construction of noncommutative [Formula: see text] black hole and its four-dimensional Yang–Mills IKKT-type matrix model which includes two competing Myers term one responsible for the condensation of pure [Formula: see text] and the other one responsible for the condensation of the dilaton field. It is argued that the...

A consistent QM/NCG duality is put forward as a model for the [Formula: see text] correspondence. This is a duality/correspondence between (1) the dAFF conformal quantum mechanics (QM) on the boundary (which is only “quasi-conformal” in the sense that there is neither an [Formula: see text]-invariant vacuum state nor there are strictly speaking pri...

The near-horizon noncommutative geometry of black holes, given by [Formula: see text], is discussed and the phase structure of the corresponding Yang–Mills matrix models is presented. The dominant phase transition as the system cools down, i.e. as the gauge coupling constant is decreased is an emergent geometry transition between a geometric noncom...

In this paper, the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is proposed in which noncommutative geometry can emerge from “one-matrix multitrace scalar matrix models” by probing...

A Gaussian approximation to the bosonic part of M-(atrix) theory with mass deformation is considered at large values of the dimension d. From the perspective of the gauge/gravity duality this action reproduces with great accuracy the stringy Hagedorn phase transition from a confinement (black string) phase to a deconfinement (black hole) phase wher...

In this article the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is proposed in which noncommutative geometry can emerge from "one-matrix multitrace scalar matrix models" by probin...

In this essay a quantum-dualistic, perspectival and synchronistic interpretation of quantum mechanics is further developed in which the classical world-from-decoherence which is perceived (decoherence) and the perceived world-in-consciousness which is classical (collapse) are not necessarily identified. Thus, Quantum Reality or "{\it unus mundus}"...

String theory provides one of the most deepest insights into quantum gravity. Its single most central and profound result is the gauge/gravity duality, i.e. the emergence of gravity from gauge theory. The two examples of M(atrix)-theory and the AdS/CFT correspondence, together with the fundamental phenomena of quantum entanglement, are of paramount...

https://iopscience.iop.org/book/978-0-7503-2600-1

The near-horizon noncommutative geometry of black holes, given by AdS^2_{\theta} x S^2_N, is discussed and the phase structure of the corresponding Yang-Mills matrix models is presented. The dominant phase transition as the system cools down, i.e. as the gauge coupling constant is decreased is an emergent geometry transition between a geometric non...

In this article we present the construction of noncommutative AdS^2_{\theta} black hole and its four-dimensional Yang-Mills IKKT-type matrix model which includes two competing Myers term one responsible for the condensation of pure AdS^2_{\theta} and the other one responsible for the condensation of the dilaton field. It is argued that the phase di...

A consistent QM/NCG duality is put forward as a model for the AdS^2/CFT_1 correspondence. This is a duality/correspondence between 1) the dAFF conformal quantum mechanics (QM) on the boundary (which is only "quasi-conformal" in the sense that there is neither an SO(1,2)-invariant vacuum state nor there are strictly speaking primary operators), and...

Parallels between the measurement problem in quantum mechanics and the black hole information loss problem in quantum gravity are exhibited and then the attempted resolution of the latter in terms of the gauge/gravity duality is extended to the former.

The Wilsonian renormalization group approach to matrix models is outlined and applied to multitrace matrix models with emphasis on the computation of the fixed points which could describe the phase structure of noncommutative scalar phi-four theory.

Quantum mechanics in the Wigner-von Neumann interpretation is presented. This is characterized by 1) a quantum dualism between matter and consciousness unified within an informational neutral monism, 2) a quantum perspectivism which is extended to a complementarity between the Copenhagen interpretation and the many-worlds formalism, 3) a psychophys...

A Gaussian approximation to the bosonic part of M-(atrix) theory with mass deformation is considered at large values of the dimension $d$. From the perspective of the gauge/gravity duality this action reproduces with great accuracy the stringy Hagedorn phase transition from a confinement (black string) phase to a deconfinement (black hole) phase wh...

Lectures delivered at Eloued University between 16/02/2020 and 20/02/2020. This includes two realistic simulations with two detailed Monte Carlo codes.

theorems of quantum philosophy, quantum logic, quantum metaphysics and interpretations of quantum mechanics.

This book deals with the interplay between fundamental physics and philosophy of physics from the one hand and metaphysics and philosophy from the other hand. It is divided into three independent parts (philosophical, general and mathematical). Part I deals with foundations and philosophy of quantum mechanics, philosophy of time, philosophy of cons...

This two-volume book was accepted for publication by IOP (Institute of Physics) on 20/02/2017, submitted on 14/12/2018 and will appear in its final form during the spring of 2019. It contains a comprehensive introduction to the fundamental topic of quantum field theory starting from free fields and their quantization, renormalizable interactions, c...

We draw systematic parallels between the measurement problem in quantum mechanics and the information loss problem in black holes. Then we proceed to propose a solution of the former along the lines of the solution of the latter which is based on the holographic gauge/gravity duality. The proposed solution is based on 1) the quantum dualism between...

We draw systematic parallels between the measurement problem in quantum mechanics and the information loss problem in black holes. Then we proceed to propose a solution of the former along the lines of the solution of the latter which is based on the holographic gauge/gravity duality. The proposed solution is based on 1) the quantum dualism between...

An overview of the gauge/gravity duality and its application to the black hole information loss problem and to the problem of the emergence of spacetime from quantum entanglement.

We are going to present throughout these lectures the basics of quantum mechanics and quantum gravity as well as some applications of quantum mechanics in different
areas namely optics.

انظروا الكتاب الجديد الواقع و الزمن و الفيزياء الاساسية الذى يحتوى على آخر ما كتبت حول فلسفة الكمومى و الزمن بالاضافة الى اشياء اخرى كثيرة. اه

This article is divided into three parts. First, a systematic derivation of the Hawking radiation is given in three different ways. The information loss problem is then discussed in great detail. The last part contains a concise discussion of black hole thermodynamics. This article was published as chapter $6$ of the IOP book "Lectures on General R...

A review of M-(atrix) theory (the BFFS matrix quantum mechanics), type IIB matrix model (the IKKT matrix model) and Matrix String Theory (the DVV matrix gauge theory) is presented.

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 2D quantum gravity which works away from two dimensions and captures a large class of spaces admiting a finite spectral triple. These multitrace matri...

This book is divided into two parts. In the first part we give an elementary introduction to computational physics consisting of 21 simulations which originated from a formal course of lectures and laboratory simulations delivered since 2010 to physics students at Annaba University. The second part is much more advanced and deals with the problem o...

In this chapter quantum noncommutative Φ⁴ theories on Moyal-Weyl spaces, the noncommutative fuzzy torus, and the fuzzy spheres S²N and S²N × S²N are presented. This includes analytical results such as the UV-IR mixing, the stripe phase, the exact solution of the self-dual theory, as well as Monte Carlo results such as the phase structure on the fuz...

In this chapter the quantization of the commutative sphere which yields the noncommutative fuzzy sphere is discussed in great detail. We explicitly construct coherent states, the star product, the flattening limit as well as noncommutative scalar field theories on the fuzzy sphere. A brief introduction to fuzzy CP² and to fuzzy fermions and Dirac o...

In this chapter we apply the powerful multitrace approach to noncommutative Φ⁴ theory on the Moyal-Weyl plane R²θΩ and on the fuzzy sphere S²N and employ random matrix theory to solve for the phase structure of the theory. Then a discussion of the planar theory is given in some detail.

This chapter contains a detailed discussion of the Heisenberg algebra and its representation theory. Then a systematic construction of the Moyal-Weyl noncommutative spaces, in a generic non-zero magnetic field, and their scalar field theories is put forward. A self-contained discussion of two other closely related non commutative space, the noncomm...

In this chapter we present a reasonably detailed introduction to noncommutative gauge theory on the Moyal-Weyl spaces Rdθ and on the noncommutative tori Tdθ. An initiation to noncommutative gauge theory on the fuzzy sphere is also included.

## Projects

Projects (3)

A series of systematic and detailed lectures at the doctoral level in theoretical physics.

A systematic study of the modern philosophy of physics (in particular the metaphysics of quantum mechanics and the philosophy of time) which is a project we have termed "experimental metaphysics". A strong connections to Metaphysics, Existentialism and the Philosophy of Mind are drawn and exhibited.
First Results: First results appeared today (12/10/2021) in the book (Philosophy and the Interpretation of Quantum Physics) published by Institute of Physics (IOP). See here
https://iopscience.iop.org/book/978-0-7503-2600-1

Noncommutative geometry (and its matrix models) presents a distinct solution to the problem of quantum gravity whereas the gauge/gravity correspondence is currently the most successful proposal for quantum gravity. The two approaches intersect within the quantum mechanics of the BFSS (or M-(atrix)) theory and also within the IKKT matrix model which should be viewed as providing the starting unifying framework.
The BFSS-type Yang-Mills quantum mechanics and the IKKT-type Yang-Mills matrix models provide a non-perturbative formulation of superstring theory and its underlying eleven-dimensional M-theory. But they also provide a quantum gravitational formulation (gravitational Feynman path integral) of Connes' noncommutative geometry (classical phase space). In other words, we should think of noncommutative geometry as a "first quantization of geometry" (classical gravity) and think of the corresponding matrix models as a "second quantization" of geometry " (quantum gravity).
Poisson manifolds play therefore the fundamental role of "curved spacetime", the Darboux theorem plays the role of the "equaivalence principle" while Moyal-Weyl spaces are what defines our "flat spacetime".
The nature of quantum geometry can also be probed by means of multitrace matrix models where both the renormalization group equation, the large N saddle point analysis and the Monte Carlo method come together in a symphony of mathematical and computational methods applied to the same theoretical problem (which is quite rare). The multitrace matrix models is in fact an alternative to Yang-Mills matrix models which allow for emergent geometry (quantum geometry), emergent gravity (quantum gravity) and emergent time (quantum cosmology).
Another important gauge/gravity duality (besides the BFSS-type Yang-Mills quantum mechanics) is the AdS/CFT correspondence. The case of two dimensions is the most mysterious and is the most important for quantum black holes as well as it is the case most closely related to noncommutative geometry which is very intriguing indeed.
Question 1: Towards "computational physics of string theory"!
Answer 1: Preliminary results are reported in https://arxiv.org/abs/2007.04488.
Question 2: What is the relation between multitrace matrix models and quantum geometry?
Answer 2A: The discussion of the fixed points of a cubic multitrace matrix model (which is important to a very important case of emergent noncommutative geometry in two dimensions, i.e. the fuzzy sphere, the noncommutative torus and the Moyal-Weyl plane) is discussed in https://arxiv.org/abs/2008.09564.
Answer 2B (Oct 2021): See update number 12 for a new comprehensive detailed answer reported in the preprint https://arxiv.org/abs/2110.06677.
Question 3: Can we reformulate a noncommutative theory of the AdS/CFT correspondence and black hole evaporation problem?
Answer 3 (Sep 2021): Update number 9 (The AdS^2_θ/CFT_1 Correspondence and Noncommutative Geometry). See also https://badisydri.blogspot.com/2021/09/the-ads2cft1-correspondence-and.html