arXiv subjects

Mir Faizal

Publications and source records attributed to Mir Faizal.

At least 19 recordsLinked to original sources

arXiv2026

Finite-Resolution Limits on Quantum Uniqueness

The Stone-von Neumann theorem makes canonical quantization unique only after one imposes strong continuity of the Weyl translation groups. We show that this continuity assumption cannot be certified by any finite-resolution interrogation of the Weyl relations. A finite protocol probes only finitely many phase-space displacements and bounded expectation values, thereby determining a protocol algebra $C_S$ generated by a finitely generated subgroup of Weyl translations, but not the regularity of an extension to the full Weyl algebra. Using the polymer representation as a canonical non-regular representation, we prove that for every regular Weyl representation, every normal state, and every finite family of bounded protocol observables, a polymer state reproduces the same expectation values to arbitrary prescribed accuracy. Thus finite agreement with Schr\"{o}dinger quantum mechanics does not operationally certify the regularity hypothesis entering uniqueness. The result does not assert physical equivalence between regular and polymer quantizations, it identifies where additional input, such as Hamiltonian dynamics, energy regularity, semiclassicality, or a continuum limit, is required to distinguish or select representations. In this precise sense, non-regular polymer kinematics are not excluded by finite Weyl data alone, a point of direct relevance to quantum-gravity motivated quantizations.

quant-ph↗

arXiv2026

A sharp bound on spacetime distance from quantum entanglement

Ryu-Takayanagi established how boundary entanglement encodes bulk area. We provide the metric counterpart: boundary mutual information imposes a rigorous lower bound on bulk geodesic separation that diverges logarithmically as correlations vanish. A multiscale iteration promotes this local inequality to a global obstruction to bulk connectivity. For parallel strips in AdS$_5$/CFT$_4$, the bound necessitates a quantum resolution of the classical mutual-information transition and fixes the asymptotic growth of geodesic distance.

hep-th↗

arXiv2026

Constructive realization of self-referential prediction limits in quantum control: Resource bounds and G\"odel-safe architectures

Programmable quantum control systems increasingly rely on predictive modules for certification, real-time feedback, and autonomous decision-making. This development raises a fundamental question: can self-analyzing quantum platforms universally predict their own experimental outcomes? Wolpert formalized a general impossibility of universal self-prediction. Here we translate that limitation into an explicit laboratory obstruction that can be realized with finite resources. We consider settings with programmable quantum control in which predictors can be embedded as subroutines within the experiments they analyze. Our diagonal construction uses Kleene's recursion theorem to transform any deterministic bounded-time predictor into a reversible protocol encoding its own specification. The resulting protocol invokes the predictor on that specification and deterministically produces a classical pointer record that contradicts the forecast. For efficient predictors, the compilation has polynomial overhead and admits concrete physical realizations as a fault-tolerant quantum circuit and as a minimal Mach-Zehnder interferometer. These realizations connect computability-theoretic self-reference to programmable quantum hardware. We also introduce and formally define G\"odel-safe architectures. These architectures block the forbidden causal path from the protocol description to an actuator that can affect the pointer during the same run. We analyze their implications for real-time quantum error correction, including the resulting expressiveness trade-offs. As quantum control loops grow in computational expressiveness, the limits of self-reference cease to be mere mathematical abstractions and become explicit engineering constraints for the reliable operation of autonomous quantum technologies.

quant-ph↗

arXiv2026

A T-Fold Black Hole in Doubled Type IIB

We construct an asymptotically flat T-fold representative of a four-dimensional dyonic black-hole charge orbit in doubled type-IIB theory. Starting from the F1-P-NS5-KKM toroidal seed, an integral parabolic T-duality monodromy is imposed on an active doubled three-torus. The non-geometric data enter only through this global patching: the Reissner-Nordstr\"om-type term is sourced by conserved four-dimensional electric and magnetic field strengths in the doubled Kaluza-Klein/winding local system, not by an internal algebraic $Q$-flux alone. Exact duality preserves the local equations, the BPS index, and the $O(6,6)$-invariant of the NS-NS/$N=4$ charge sublattice governing the entropy. The minimal Einstein-Maxwell-dilaton slice contains a running-scalar branch and an equal-charge Reissner-Nordstr\"om limit; the extremal near-horizon region is locally $\mathrm{AdS}_2\times S^2$, with the compact factor globally T-duality patched.

hep-th↗

arXiv2026

Reflection-Positive Construction of a Four-Dimensional SU(N) Yang-Mills Theory with Mass Gap and Confinement

In the Euclidean view one must first require that positivity not be violated, and from this modest demand, together with locality, a great deal follows: starting from a reflection-positive lattice formulation of pure SU(N) Yang-Mills theory we obtain a transfer operator with a uniform gap, while large Wilson loops already show an area law by means of convergent character (polymer) expansions; a finite-range, gauge-covariant multiscale analysis then carries these features from one scale to the next with interlaced inequalities whose small defects can be summed, so that exponential clustering and a strictly positive string tension endure in the continuum; the Osterwalder-Schrader reconstruction turns these Euclidean facts into a Minkowski theory with a self-adjoint Hamiltonian, the spectral gap lying above the vacuum and the linear potential for static charges appearing, which gives a concrete picture of confinement; the construction depends on no special regulator, for a single-scale Lipschitz control and a telescoping argument bind all admissible reflection-positive slicings into a unique limiting measure and thus secure universality; moreover, the same framework admits entry from weak coupling, so that the continuum reached from strong coupling meets the one approached along an asymptotically free trajectory, yielding one and the same theory; in my view this is how mathematical clarity and physical insight cooperate: positivity, locality, and renormalization working together so that the mass gap and confinement are not marvels to be assumed, but natural properties of the non-Abelian vacuum.

hep-lat↗

arXiv2026

Chern-Simons couplings, modular duality, and anomaly cancellation in abelian F-theory

F-theory compactifications with a nontrivial Mordell-Weil group realize abelian gauge symmetry through rational sections, but their consistency is ultimately a statement about the quantum effective action. We show that compactification on a circle makes this statement concrete: the quantized, parity-odd Chern-Simons couplings of the resulting three-dimensional theory provide a one-loop exact and scheme-independent encoding of all local four-dimensional abelian anomalies, including the mixed gauge-gravitational terms, together with their Green-Schwarz cancellation. We determine these Chern-Simons couplings in two logically independent ways, first from flux-induced terms in the M-theory dual description, and second from an explicit one-loop integration over the complete massive spectrum, including Kaluza-Klein towers and Coulomb-branch states. The agreement fixes all normalizations and clarifies how large gauge transformations reorganize the spectrum. We then show compatibility with type IIB modular duality once the known ten-dimensional duality counterterm is included, and we present a fully explicit rank-two example over projective three-space.

hep-th↗

arXiv2026

Geometric Baryogenesis with Chiral-Time Equivalence

The asymmetry between matter and antimatter demands a cause as simple as it is profound. Here we show that a single geometric principle Chiral-Time Equivalence (CTE)-suffices to generate and correlate the required CP violation with the time orientation of the cosmos. Promoting the Immirzi parameter to a pseudoscalar Nambu-Goldstone field $\Phi$, CTE fixes the leading operators: a shift-symmetric derivative portal $((\partial_\mu\Phi)J^\mu_{B-L}/M_*)$ that acts as a dynamical chemical potential in FRW, and a topological term $(\Phi\,R\tilde R)$ that imprints parity on tensor modes. In thermal equilibrium this structure produces gravity-assisted leptogenesis, whose magnitude is set at the decoupling temperature by susceptibilities rather than by tuned departures from equilibrium. A fully flavored Boltzmann network with curvature sources captures flavor transfer and washout, while slow-roll and resonant regimes are established via thermodynamic and Kubo formulas. Consistency is secured by an EFT analysis (stability, perturbative unitarity, and BBN safety), and by explicit elimination of EC torsion and control of dCS birefringence in the small-coupling domain. The most striking prediction is a sign locking among $\eta_B$, tensor chirality $\chi_T$, and the drift of $\Phi$, together with a tri-observable relation that ties $\eta_B$ to cosmic birefringence $\Delta\alpha$ and $\chi_T$. Thus a single, symmetry-protected geometric origin renders the baryon excess testable by TB/EB correlations and stochastic-wave chirality, and calculable within a minimal, ultraviolet-anchored effective theory.

hep-ph↗

arXiv2026

A symplectic geometric origin of universal quartic modified dispersion relations

We show that quartic modifications of relativistic dispersion relations arise generically from deformation-quantized phase spaces under minimal kinematical assumptions relevant to quantum gravity. When the kinematics admits an integral symplectic structure, a compatible almost-complex structure, and a gauge-invariant two-form sector, the leading Planck-scale correction is controlled by a single geometric length scale. We establish this result through three independent approaches: Fedosov-Berezin quantization, spectral geometry, and a topos-theoretic formulation, all of which yield the same quartic correction and clarify the origin of its apparent universality.

math-ph↗

arXiv2026

Discrete \texorpdfstring{$\theta$}{theta} Projection: A Gauge-Protected Solution to the Strong CP Problem Without Axions

We address the strong CP problem: why the physical QCD angle theta-bar must be extraordinarily small given the stringent bounds on the neutron electric dipole moment. Peccei-Quinn axion models can relax theta-bar dynamically, but rely on an approximate global symmetry expected to be violated by quantum gravity and face severe astrophysical and cosmological constraints. We propose Discrete theta Projection, an axionless, gauge-protected resolution obtained by gauging a finite cyclic subgroup $Z_N $of the $2\pi$ shift symmetry of theta. Coupling QCD to a compact, local and gapped topological sector orbifolds the path integral, identifying theta values that differ by $2\pi/N$ and admitting only instanton sectors whose topological charge lies in $Z_N$. In the large four-volume limit the vacuum energy becomes the lower envelope of the orbifold images, so the theory dynamically selects the branch closest to the CP-symmetric point, enforcing $|\bar{\theta}| \le \pi/N$ without assuming any prior smallness. Because the discrete shift is gauged, continuous renormalization of theta is forbidden; the construction can be formulated via higher-form/two-group structure with integer-quantized couplings fixed by anomaly inflow, ensuring radiative and gravitational stability and satisfying mixed gauge-gravity consistency conditions. The framework predicts a neutron EDM suppressed by $1/N$, no axion signatures, no domain-wall/isocurvature issues, and lattice diagnostics: piecewise-analytic theta dependence with cusps at odd fractions of the reduced period and a global curvature scaling as $1/N^2$. We provide the EFT construction, a nonperturbative proof of vacuum projection, a full anomaly analysis, and UV embeddings (including discrete clockwork chains) that generate large effective N while preserving integrality and consistency throughout.

hep-th↗

arXiv2026

A Perfectoid Duality Between M-Theory and F-Theory

We present a non-singular, definition-level formulation of F-theory by replacing the traditional shrinking-fiber limit of M-theory with compactification on a tower-completed circle described using perfectoid geometry and condensed mathematics. This construction provides an intrinsic eleven-dimensional carrier for modular data and admits a canonical tilting and comparison procedure that yields elliptic geometry as an output rather than an auxiliary input. Using this framework, we establish a precise M-theory/Type IIB dictionary in the constant-coupling sector, showing how the physical axio-dilaton is fixed by eleven-dimensional geometric and topological data. The correspondence is tested at the level of the ten-dimensional bosonic effective action, including its topological couplings inherited from eleven dimensions. The tower-completed geometry naturally organizes global sectors in generalized cohomology, with charge data governed by K-theory and exhibiting a canonical prime-power torsion structure. We further show how this framework extends to varying-coupling backgrounds and duality defects, admits a natural adelic completion with prime-independence, and generalizes to higher-rank and U-duality geometries. We also discuss holographic aspects and the anomaly-refined extension of the duality group beyond the bosonic truncation. Together, these results provide a coherent, non-singular foundation for F-theory and its extensions.

hep-th↗

arXiv2026

Time uncertainty and fundamental sensitivity limits in quantum sensing: application to optomechanical gravimetry

High-sensitivity accelerometers and gravimeters, achieving the ultimate limits of measurement sensitivity are key tools for advancing both fundamental and applied physics. While numerous platforms have been proposed to achieve this goal, from atom interferometers to optomechanical systems, all of these studies neglect the effects of intrinsic quantum uncertainty in time estimation. Starting from the Hamiltonian of a generic linear quantum sensor, we derive the two-parameter quantum Fisher information matrix and establish the corresponding Cram'er-Rao bound, treating time as an uncertain (nuisance) parameter. Our analysis reveals a fundamental coupling between time and signal estimation that inherently degrades measurement sensitivity, with the standard single-parameter quantum limit recovered only at specific interrogation times or under special decoupling conditions. We then apply these results to an optomechanical gravimeter and explicitly derive an optimal decoupling condition under which the effects of time uncertainty are averaged out in a continuous measurement scheme. Our approach is general and can be readily extended to a broad class of quantum sensors.

quant-ph↗

arXiv2026

Undecidability in Spacetime Geometry via the AdS/CFT Correspondence

Undecidability, a hallmark of G\"odel incompleteness theorems, has recently emerged in quantum many-body physics through the spectral gap problem. We demonstrate how this logical limitation can be holographically transmitted to a class of gravitational theories via the AdS/CFT correspondence. By embedding a translationally invariant spin Hamiltonian with undecidable gap status into a large-N gauge theory, we generate an AdS dual in which the selection of dominant bulk saddle (Poincar\'e AdS or AdS soliton) is itself undecidable. Consequently, under standard semiclassical holographic assumptions, even determining which smooth spacetime geometry emerges from quantum gravity can be beyond the limits of computability.

hep-th↗

arXiv2025

Unified Functional-Holographic Theory of the QCD Critical End Point

We develop a thermodynamically consistent nonperturbative framework for equilibrium QCD criticality, unifying DSE quark propagation, FRG flow, and PNJL thermodynamics for coupled chiral/deconfinement order parameters. A holographic Maxwell-Chern-Simons sector supplies topological response; its topological susceptibility enters the FRG flow of the determinantal ('t Hooft) interaction, encoding axial-anomaly evolution across the phase diagram. At $\mu_B=0$ we anchor to continuum-extrapolated lattice thermodynamics and conserved-charge susceptibilities through a lattice-calibrated Polyakov sector, enforcing exact thermodynamic identities by evaluating derivatives at the stationary grand-potential solution at each RG scale. Solving the coupled DSE-FRG-holographic system yields, at the present approximation level, an equilibrium critical end point at $T_{\mathrm{CEP}}\simeq130\text{--}135,\mathrm{MeV}$ and $\mu_{B,\mathrm{CEP}}\simeq600,\mathrm{MeV}$, with quantified sensitivity to regulator, Polyakov-sector, and holographic-normalization choices. The critical region is organized by a nonperturbative map onto universal 3D Ising scaling variables, with anomalous-dimension effects absorbed into nonuniversal metric factors, yielding predictions for the hierarchy, nonmonotonicity, and sign structure of higher-order net-baryon cumulant ratios along smooth freeze-out trajectories and speed-of-sound softening. Comparisons to RHIC BES fluctuation measurements are qualitative consistency checks on correlated equilibrium trends and sign patterns, because finite size/lifetime, critical slowing down, baryon-number conservation, acceptance/efficiency corrections, net-proton-to-net-baryon conversion, and baryon transport can round or reshape experimental cumulants. The results provide a unified equilibrium baseline and controlled inputs for finite-size scaling and dynamical embeddings of heavy-ion data.

hep-ph↗

arXiv2025

Propagation-Distance Limit for a Classical Nonlocal Optical System

We derive closed-form analog quantum-speed-limit (QSL) bounds for highly nonlocal optical beams whose paraxial propagation is mapped to a reversed (inverted) harmonic-oscillator generator. Treating the longitudinal coordinate $z$ as an evolution parameter (propagation distance), we construct the propagator, evaluate the Bures distance, and obtain analytic Mandelstam--Tamm and Margolus--Levitin bounds that fix a propagation-distance limit $z_{\mathrm{PDL}}$ to reach a prescribed mode distinguishability. This distance-domain constraint is the classical optical analogue of the minimal orthogonality time in quantum mechanics. We then propose a compact self-defocusing PDL beam shaper that achieves strong transverse-mode conversion within millimeter scales. We further show that small variations in refractive index, beam power, or temperature shift $z_{\mathrm{SL}}$ with high leverage, enabling speed-limit-based metrology with index sensitivities down to $10^{-7}$ RIU and temperature resolutions of order $1$ mK. The results bridge distance-domain QSL geometry and practical photonic applications.

quant-ph↗

arXiv2025

Relativistic Quantum-Speed Limit for Gaussian Systems and Prospective Experimental Verification

Timing and phase resolution in satellite QKD, kilometre-scale gravitational-wave detectors, and space-borne clock networks hinge on quantum-speed limits (QSLs), yet benchmarks omit relativistic effects for coherent and squeezed probes. We derive first-order relativistic corrections to the Mandelstam-Tamm and Margolus-Levitin bounds. Starting from the Foldy-Wouthuysen expansion and treating $-p^{4}/(8 m^{3} c^{2})$ as a harmonic-oscillator perturbation, we propagate Gaussian states to obtain closed-form QSLs and the quantum Cram\'er-Rao bound. Relativistic kinematics slow evolution in an amplitude- and squeezing-dependent way, increase both bounds, and introduce an $\epsilon^{2} t^{2}$ phase drift that weakens timing sensitivity while modestly increasing the squeeze factor. A single electron ($\epsilon \approx 1.5\times 10^{-10}$) in a $5.4\,\mathrm{T}$ Penning trap, read out with $149\,\mathrm{GHz}$ quantum-limited balanced homodyne, should reveal this drift within $\sim 15\,\mathrm{min}$ -- within known hold times. These results benchmark relativistic corrections in continuous-variable systems and point to an accessible test of the quantum speed limit in high-velocity or strong-field regimes.

quant-ph↗

arXiv2025

Universal work statistics in quenched gapless quantum systems

We study the universality of work statistics performed during a quench in gapless quantum systems. We show that the cumulants of work scale separately in the fast and slow quench regimes, following a power law analogous to the universal scaling in the Kibble-Zurek mechanism for topological defect formation in phase transition. As an example, we analyze the nonequilibrium dynamics of a quenched Heisenberg XXZ chain at its critical gapless state using the bosonization picture, resulting in a Tomonaga-Luttinger liquid. The analytical scaling is in agreement with the exact numerical calculation for the fast and slow quench regimes. In finite systems, the characteristic function display an oscillatory pattern which disappears in the thermodynamic limit. This study is particularly useful for understanding the thermodynamics of adiabatic quantum computation.

quant-ph↗

arXiv2025

Consequences of Undecidability in Physics on the Theory of Everything

General relativity treats spacetime as dynamical and exhibits its breakdown at singularities. This failure is interpreted as evidence that quantum gravity is not a theory formulated within spacetime; instead, it must explain the very emergence of spacetime from deeper quantum degrees of freedom, thereby resolving singularities. Quantum gravity is therefore envisaged as an axiomatic structure, and algorithmic calculations acting on these axioms are expected to generate spacetime. However, G\"odel's incompleteness theorems, Tarski's undefinability theorem, and Chaitin's information-theoretic incompleteness establish intrinsic limits on any such algorithmic programme. Together, these results imply that a wholly algorithmic "Theory of Everything" is impossible: certain facets of reality will remain computationally undecidable and can be accessed only through non-algorithmic understanding. We formalize this by constructing a "Meta-Theory of Everything" grounded in non-algorithmic understanding, showing how it can account for undecidable phenomena and demonstrating that the breakdown of computational descriptions of nature does not entail a breakdown of science. Because any putative simulation of the universe would itself be algorithmic, this framework also implies that the universe cannot be a simulation.

gr-qc↗

arXiv2025

A Novel Construction of de Sitter Vacua in Heterotic String Theory

We present a concrete string-theoretic mechanism that generates four-dimensional de Sitter vacua from non-geometric R-flux compactifications of heterotic string theory. The construction rests on three pillars: the Malcev algebra generated by the R-flux phase-space brackets; its universal Sabinin envelope, which ensures a consistent non-associative gauge structure in doubled geometry; and the leading alpha-prime torsion-squared correction to the heterotic action, whose strictly positive contribution uplifts the scalar potential. Positivity, guaranteed by Sabinin-algebra identities, stabilizes the overall breathing mode at positive energy, yielding a controlled metastable de Sitter scenario within heterotic effective field theory when supplemented by a standard hidden-sector gaugino-condensation uplift.

hep-th↗