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Badis Ydri

Publications and source records attributed to Badis Ydri.

At least 19 recordsLinked to original sources
arXiv2026

Latent Geometry and the Emergence of Lorentzian Time in Matrix Quantum Mechanics

We introduce \emph{latent geometry} in BFSS/BMN models. Before an emergent geometry evaporates at the geometric transition, large-$d$ Gaussianization encodes its information in the exceptional $N=2$ sector selected by the baby fuzzy sphere, a single active spin-$1/2$ Pauli block. Dimensional reduction, finite-$N$ Gaussianization and exact Molien--Weyl projection transport this encoding to mass-deformed BFSS$_2$. At $N=2$, the same stable BFSS$_2$ oscillator admits inequivalent unitary $\mathbf{H}^2_\theta=\mathbf{EAdS}^2_\theta$ and $\mathbf{dS}^2_\theta$ decodings, realizing spacetime transmutation and the emergence of Lorentzian time.

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arXiv2026

Gram--Wishart--Stiefel formulation of the $N=2$, large--$d$ gauge theory in 1D

We develop in this paper the Gram/Wishart/Stiefel formulation of the \(N=2\), large--\(d\) planar endpoint theory of the BFSS/BMN matrix quantum mechanics on the lattice, obtained in our previous work. In this formulation, the endpoint degrees of freedom are reorganized into rank--two Wishart eigenvalues and relative Stiefel angular variables. This allows the holonomy invariants \(A\), \(B\), and \(R^2=A^2+B^2\) to be analyzed directly in terms of radial and angular Gram data. A central point is the large-\(R\) aligned asymptotics of the holonomy potential. Its universal linear contribution \(-A\) is absorbed into the Gaussian sector, producing the shifted mass parameter \((\alpha_\Lambda)_{\rm eff}=\alpha_\Lambda-1/2\). In the Gram/Wishart/Stiefel variables, the exact \(O(2)\) angular integral encodes this shifted sector in a rank--two Bessel kernel. The pure \(-A\) theory, which is exactly solvable in Cartesian variables, then fixes the leading Bessel/HCIZ structure: its exponential part selects the aligned configuration, while its prefactor removes the spurious doubled Wishart entropy. We then apply this structure to the transverse \(B\)-type expansion and its non-polynomial toy completion. Finite polynomial truncations lead to an apparent large--\(d\) perturbativity bound incompatible with the continuum limit, but this bound is shown to be an artifact of truncation. After summing the local transverse completion and balancing the compensating \(+A\) term, the Wishart saddle is recovered with the physical shifted mass. The resulting continuum behavior reproduces the universal \(-2d\) contribution of the \(D_\Lambda\)-channel, while the genuinely anisotropic \(\beta_\Lambda\)-channel lies outside the scope of a pure transverse \(B\)-type description.

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arXiv2026

A Double--Scaling Large--\(d\) Saddle of BFSS/BMN Matrix Quantum Mechanics

We study the large--\(d\) dynamics of the mass--deformed bosonic \(\mathrm{BFSS}_{d+1}\) matrix quantum mechanics using a Hubbard--Stratonovich localization of the Yang--Mills interaction. After integrating out the matrix coordinates, the theory reduces to a holonomy--dependent effective action for an auxiliary adjoint kernel. We introduce a commuting--symmetric saddle and its maximally symmetric specialization, in which the interaction is encoded in a single dynamically generated mass shift \(k_0\). The resulting large--\(d\) description is a gauged matrix harmonic oscillator with self--consistent frequency \(s^2=m+k_0\), fixed by a gap equation. We analyze the low--temperature \(X\)-space physics, the holonomy effective action, the Yang--Mills observable, and the associated phase structure. We then identify a correlated double--scaling limit in which \(d\to\infty\), \(m\to\infty\), and \(\kappa=m^{3/2}/d\) is held fixed. In this limit the Yang--Mills interaction and the explicit mass deformation remain parametrically balanced: the theory interpolates between the commutator--dominated BFSS regime and the mass--dominated Gaussian regime. The double--scaled theory exhibits two complementary large--\(d\) regimes. At low temperature, the enhanced gap pushes the deconfinement scale upward and opens a parametrically large uniform--holonomy region, where the bulk dynamics behaves as weakly coupled \(\mathrm{BFSS}_2\)--type gauged harmonic--oscillator sectors. At the same time, the high--temperature branch reveals an overlap window in which the Gaussian description remains self--consistent while the commutator contribution per matrix pair is parametrically suppressed. The resulting dynamics is therefore \(\mathrm{BFSS}_2\)--like in its enlarged uniform--holonomy sector and IKKT--like in its almost--commuting matrix behavior.

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arXiv2026

Endpoint formulation and Molien--Weyl structure for the \(N=2\), large--\(d\) BFSS/BMN models

We study the \(N=2\), large--\(d\) sector of BFSS/BMN-type matrix quantum mechanics on the lattice in the Gaussian regime. We develop a radial endpoint formulation in which the bulk, gauge, and longitudinal degrees of freedom are integrated out, leaving transverse endpoint variables governed by an effective holonomy potential. We show that this planar endpoint formulation is equivalent to the angular Molien--Weyl description of the gauge-projected partition function, up to a universal spectator factor. This relation allows the low-temperature expansion of the endpoint partition function to be obtained from the Molien--Weyl result, whose quadratic coefficient \(d(d+1)/2\) counts Gaussian singlet states above the vacuum. We then analyze the continuum limit of the quadratic coefficient and show that it separates into a Gaussian contribution, a \(D\)-channel, and a \(\beta\)-channel. The naive Gaussian term becomes trivial, while the exact holonomy kernel generates finite continuum contributions through singular dependence on the endpoint Gaussian width and anisotropic coupling. We then study the geometry of the holonomy potential and show that its relevant saddle is a constrained boundary saddle on the aligned branch, rather than an unconstrained critical point. The associated transverse expansion captures the local saddle geometry, but any finite polynomial truncation has a trivial continuum limit. Finally, we introduce a non-polynomial toy model based on \(V_{\rm toy}(B)=-\log\cosh B\), which provides a completion of the transverse expansion and reproduces exactly the continuum \(D\)-channel contribution \(-2d\). This prepares the geometric interpretation of the \(D\)-channel as a Wishart--Stiefel entropy associated with an emergent four-dimensional geometry embedded \(\mathbb R^d\) in the endpoint formulation.

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arXiv2026

Molien--Weyl Singlet Counting and BFSS$_2$--Factorization in Gaussian Matrix QM

We study the singlet-sector structure of mass-deformed BFSS$_{d+1}$ matrix quantum mechanics by combining the large--\(d\) Gaussian reduction with the Molien--Weyl projection. The Gaussian reduction captures the bulk matrix dynamics through a gauged harmonic oscillator, while the Molien--Weyl integral imposes the Gauss law and reorganizes the physical Hilbert space into holonomy-projected singlet excitations. We show that the very-low-temperature bosonic singlet spectrum is universally controlled by the quadratic Gram operators \(\Tr(X_aX_b)\), whose number is \(d(d+1)/2\). For \(N=2\), this result is established by explicit residue computations and character methods; for \(N>2\), it is supported by the character analysis. Thus the infrared spectrum begins as a collection of BFSS$_2$--like Gram towers, although higher invariant structures generally modify the full partition function. We also give a Hamiltonian derivation of the exceptional exact factorization at \((d,N)=(2,2)\), where the BFSS$_3$ singlet partition function equals the cube of the BFSS$_2$ one for all temperatures. This rigidity is special to the \(SU(2)\) invariant tensor structure and explains why \(d=1\) and \(N=2\) are exceptional regimes without a deconfinement crossover. Finally, we extend the Gram-counting picture to supersymmetric BFSS/BMN models and indicate how the Molien--Weyl formulation can benchmark Monte Carlo simulations in both \(X_a\)-space and holonomy space.

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arXiv2025

Quantum Black Holes and Gauge/Gravity Duality

From a conceptual point of view, this chapter may be viewed as an exercise in combining quantum field theory and general relativity in a controlled setting. Despite its apparent simplicity, this exercise is deeply rooted in highly non-trivial developments in superstring theory and holography, and it addresses what is arguably one of the most profound questions in quantum gravity: the fate of information in black hole evaporation. For this reason, one is naturally compelled to examine this exercise as carefully as possible, closely following the original authors. This chapter presents thus a detailed overview of recent work by Almheiri et al. and Penington on the AdS2 black hole information loss paradox and its proposed resolution within the framework of the AdS/CFT correspondence. The roles of generalized entanglement entropy, quantum extremal surfaces, the island conjecture, holography, and replica wormholes in this resolution are discussed in detail. The distinction between the von Neumann entropy and the Bekenstein-Hawking entropy in black hole physics is carefully clarified. It is shown that a phase transition at the Page time, between the trivial quantum extremal surface at the horizon and a non-vanishing quantum extremal surface located behind the horizon, leads to the correct Page curve. A simplified version of the information loss problem for the eternal AdS2 black hole, together with its resolution along similar lines, is also presented. The replica trick and its crucial role in computing entanglement entropies for various intervals in AdS2 are discussed at some length. However, the use of the replica trick in constructing replica wormholes that dominate the Euclidean path integral, thereby leading to the island rule and the correct quantum extremal surfaces, is only outlined.

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arXiv2025

Novel Phenomena in Noncommutative Field Theory: Emergent Geometry

Noncommutative field theory (NCFT) is an extension of quantum field theory (QFT) that redefines spacetime, replacing commuting coordinates with a noncommutative structure. This shift fundamentally alters the way fields, interactions, and symmetries are understood. NCFT uniquely integrates with supersymmetry, making it a natural framework for unifying quantum mechanics and gravity. It also provides a consistent mechanism for spontaneous supersymmetry breaking. Unlike conventional QFT, which quantizes fields on a fixed spacetime, NCFT begins by quantizing spacetime itself. This perspective reveals novel phenomena, such as ultraviolet-infrared mixing and a natural transition from discrete to continuous geometries. It offers insights into quantum gravity at the Planck scale. Mathematically, NCFT bridges quantum mechanics and geometry through operator algebras, enabling the exploration of new theories unattainable in traditional frameworks. This dual role cements NCFT as a cornerstone of modern theoretical physics. The presentation is comprehensive and pedagogical in nature, and may contain textual overlap with earlier preprints by the author; its aim is to provide a unified and hopefully more fundamental treatment connecting results and viewpoints not previously treated together.

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arXiv2025

Quantum Perspectivism vs Nietzschean Perspectivism

This is a work of hard physical philosophy, where Quantum Perspectivism is shown to function as both an interpretation of quantum mechanics and a physical model for understanding Nietzsche's perspectivism. This framework combines quantum logic, the principle of complementarity, and contextuality to examine how perspectives construct reality. In this model, measurements correspond to Perspectives and Meta-Perspectives, represented as Boolean subalgebras and Hilbert sub-lattices within the Hilbert lattice, respectively. The Hilbert lattice itself is reinterpreted as Jung's Unus Mundus, a unified ontological reality. A metaphysical observation, made by a metaphysical observer, of a given system (World) is identified with the set of all corresponding meta-perspectives in the Hilbert lattice/Unus Mundus, the ocean of reality. Perspectives, likened to islands in this ocean, correspond to single measurements of a system, capturing the logical structure of observed properties. Meta-perspectives, analogous to continents, represent the synthesis of multiple measurements, providing a broader yet inherently incomplete understanding of the system. This structure emphasizes the complementarity and contextual dependencies of measurements while exposing the limitations of classical objectivity in the quantum domain. Advocating for a perspectival view of both the world and truth, Quantum Perspectivism unites quantum mechanics and Nietzschean philosophy into a cohesive framework for exploring the interplay between consciousness, observation, and reality.

physics.hist-ph↗
arXiv2022

The QM/NCG Correspondence

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 black holes and emergent geometry/gravity are also discussed.

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arXiv2022

Monte-Carlo simulation of the Gaussian BFSS matrix model at large number of dimensions

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 parameter to investigate the large-N behavior of this model at different temperatures, other observables such as internal energy and extent of space were also computed. In the last part, we present the matrix-geometry approach to a modified action where we captured only a remnant of the geometric Yang-Mills to a baby-fuzzy-sphere phase where the fuzzy sphere solution is only manifested as a three-cut configuration. The Yang-Mills phase retains most of its characteristics with two exceptions: i) the uniform distribution inside a solid ball suffers a crossover at very small values of the gauge coupling constant to a Wigner's semi-circle law, and ii) the uniform distribution at small T is non-existent.

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arXiv2021

Bell's theorem: A bridge between the measurement and the mind/body problems

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}" is seen as both i) a physical non-perspectival causal Reality where the quantum-to-classical transition is operated by decoherence, and as ii) a quantum linear superposition of all classical psycho-physical perspectival Realities which are governed by synchronicity as well as causality (corresponding to classical first-person observes who actually populate the world). This interpretation is termed the Nietzsche-Jung-Pauli interpretation and is a re-imagining of the Wigner-von Neumann interpretation which is also consistent with some reading of Bohr's quantum philosophy.

physics.hist-ph↗
arXiv2021

Quantized Noncommutative Geometry from Multitrace Matrix Models

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 probing the statistical physics of commutative phases of matter. This is in contrast to the usual mechanism in which noncommutative geometry emerges from "many-matrix singletrace Yang-Mills matrix models" by probing the statistical physics of noncommutative phases of gauge theory. In this novel scenario quantized geometry emerges in the form of a transition between the two phase diagrams of the real quartic matrix model and the noncommutative scalar phi-four field theory. More precisely, emergence of the geometry is identified here with the emergence of the uniform-ordered phase and the corresponding commutative (Ising) and noncommutative (stripe) coexistence lines. The critical exponents and the Wigner's semicircle law are used to determine the dimension and the metric respectively. Arguments from the saddle point equation, from Monte Carlo simulation and from the matrix renormalization group equation are provided in support of this scenario.

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arXiv2021

On the AdS/CFT correspondence and quantum entanglement

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 importance to many fundamental problems including the physics of black holes (in particular to the information loss paradox), the emergence of spacetime geometry and to the problem of the reconciliation of general relativity and quantum mechanics. In this article an account of the AdS/CFT correspondence and the role of quantum entanglement in the emergence of spacetime geometry using strictly the language of quantum field theory is put forward.

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arXiv2021

The AdS^2_{\theta}/CFT_1 Correspondence and Noncommutative Geometry III: Phase Structure of the Noncommutative AdS^2_{\theta} x S^2_N

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 noncommutative AdS^2_{\theta} x S^2_N phase (discrete spectrum) and a Yang-Mills matrix phase (continuous spectrum) with no background geometrical structure. We also find a possibility for topology change transitions in which space or time directions grow or decay as the temperature is varied. Indeed, the noncommutative near-horizon geometry AdS^2_{\theta} x S^2_N can evaporate only partially to a fuzzy sphere S^2_N (emergence of time) or to a noncommutative anti-de Sitter spacetime AdS^2_{\theta} (topology change).

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arXiv2021

The AdS^2_{\theta}/CFT_1 Correspondence and Noncommutative Geometry II: Noncommutative Quantum Black Holes

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 diagram of this matrix model features three phases: 1) A gravitational phase (AdS^2_{\theta} black hole), 2) A geometric phase (AdS^2_{\theta} background) and 3) A Yang-Mills phase. The Hawking process is therefore seen as an exotic line of discontinuous transitions between the gravitational and geometrical phases. Alternatively, a noncommutative non-linear sigma model describing the transition of the dilaton field between the gravitational and geometrical phases is also constructed.

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arXiv2021

The AdS^2_{\theta}/CFT_1 Correspondence and Noncommutative Geometry I: A QM/NCG Correspondence

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 between 2) the noncommutative geometry of AdS^2_{\theta} in the bulk (which is only "quasi-AdS" in the sense of being only asymptotically AdS^2). The Laplacian operators on noncommutative AdS^2_{\theta} and commutative AdS^2 have the same spectrum and thus their correlators are conjectured to be identical. These bulk correlation functions are found to be correctly reproduced by appropriately defined boundary quantum observables in the dAFF quantum mechanics. Moreover, these quasi-primary operators on the boundary form a subalgebra of the operator algebra of noncommutative AdS^2_{\theta}.

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arXiv2020

Black Hole Interpretation of Quantum Mechanics

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.

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arXiv2020

Wilsonian Matrix Renormalization Group

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.

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