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Farrukh A. Chishtie

Publications and source records attributed to Farrukh A. Chishtie.

16 recordsLinked to original sources
arXiv2026

Theoretical and experimental assessment of Einstein-Cartan theory: A comparative analysis within the USMEG-EFT framework

The Unified Standard Model with Emergent Gravity (USMEG-EFT) framework achieves Standard Model-gravity unification by treating 4D General Relativity as an effective field theory. This work presents a comparative analysis of Einstein-Cartan (EC) theory and USMEG-EFT against experimental constraints and theoretical consistency requirements, distinguishing minimal EC with algebraically determined torsion from variants in which the spin connection is an independent quantum field. The latter class includes the Faddeev-Popov quantization framework of Brandt, Frenkel, Martins-Filho and McKeon adopted in their unification proposal, and for it gravitational wave polarization measurements directly test the additional propagating degrees of freedom. General relativity's spin-2 graviton produces exactly two tensor polarizations, while EC theory with independent dynamical spin connection predicts up to six modes. LIGO-Virgo-KAGRA null tests for GW170817 favor pure tensor over pure vector and pure scalar hypotheses at Bayes factors exceeding $10^{20}{:}1$, improved to approximately $10^{26}{:}1$ with a gamma-ray-burst jet-orientation prior. Complementary matter-sector constraints from the Standard Model Extension yield $|\tilde{b}^n_\perp| < 8.4 \times 10^{-34}$ GeV, constraining background-torsion scenarios, while MICROSCOPE bounds equivalence principle violation at $η< 1.5 \times 10^{-15}$. For minimal EC theory, the four-fermion contact interaction generated upon coupling to fermions introduces non-renormalizable divergence structures at two-loop order, a case not addressed by the BRST framework established for the independent spin connection. We situate EC theory within the broader landscape of gauge gravity theories and acknowledge USMEG-EFT's limitations, including sub-Planckian validity and currently untestable distinctive predictions.

physics.gen-ph↗
arXiv2026

Classical spacetime as a gravitational condensate: USMEG-EFT emergence in comparison to Verlinde's entropic gravity

We present a derivation showing that classical spacetime geometry is a \emph{gravitational condensate} within the Unified Standard Model with Emergent Gravity--Effective Field Theory (USMEG-EFT): the background metric $\barg_{μν}$ is the vacuum expectation value of the quantum metric operator, existing as an ordered phase below the gravitational breakdown scale $\Lgrav \sim 10^{18}$\,GeV. The condensed phase is characterized by a nondegenerate metric expectation value, a diffeomorphism-invariant criterion whose controlled realization is confined to scales below $\Lgrav$. Three convergent quantum-field-theoretic analyses within the framework, namely canonical covariance breakdown \cite{Chishtie23}, one-loop renormalization group analysis \cite{Chishtie25CJP}, and conditional BRST closure \cite{ChishtieSymmetry26}, identify this scale as the boundary of the controlled geometric description. We show that the condensate order parameter, defined via the Legendre transform of the Lagrange multiplier path integral \cite{BrandtFrenkelMcKeon20,McKeonBrandt25}, satisfies a quantum-corrected saddle-point equation whose one-loop correction grows to the size of the tree term at $\Lgrav$, beyond which the framework supplies no controlled nondegenerate solution; we interpret this boundary as the onset of condensate dissolution. Because the Lagrange multiplier constraint acts on virtual graviton fluctuations and terminates the gravitational sector exactly at one loop, this boundary arises from a finite, closed set of quantum corrections, in contrast to the gradual failure of the derivative expansion in the standard effective field theory treatment of general relativity \cite{Donoghue94}. This mechanism is fundamentally distinct from, and resolves known inconsistencies of, Verlinde's entropic gravity programme.

physics.gen-ph↗
arXiv2026

Sensitivity of Standard Model Vacuum Stability to Enhanced Scalar Couplings: A Coupling Scan and its Implications for Radiatively Broken Electroweak Symmetry

We study how Standard Model vacuum stability depends on the Higgs quartic coupling at the electroweak matching scale, parameterized through a dimensionless enhancement factor $k = λ_{\rm enhanced}(M_t)/λ_{\rm SM}(M_t)$, with the observed Higgs mass held fixed at $M_h = 125$~GeV. This is a scan of the coupling itself, treated as a free parameter set by physics beyond the Standard Model, and is distinct from the Higgs-mass scan that underlies the conventional stability bound. Using the complete three-loop renormalization group equations including all gauge and Yukawa couplings, we find a critical threshold $k_{\rm crit} \approx 1.076$ separating the metastable Standard Model trajectory from absolutely stable trajectories. At this threshold the matching-scale coupling is $λ(M_t) \approx 0.135$, which reproduces the established three-loop absolute-stability boundary, providing an internal consistency check of the framework. The instability scale is highly sensitive to $k$ near the threshold, with a logarithmic susceptibility $d\lnΛ_I/d\ln k$ of order $10^3$ as $k \to k_{\rm crit}^-$, larger by two to three orders of magnitude than the analogous susceptibility of $Λ_{\rm QCD}$ to $α_s(M_Z)$. For $k > k_{\rm crit}$ the vacuum is absolutely stable and $λ$ develops an ultraviolet Landau pole whose scale falls rapidly with increasing $k$: for moderate enhancement the pole lies near the Planck scale, while for the large enhancement $k \approx 7.2$ associated with radiative electroweak symmetry breaking the matching-scale coupling is $λ(M_t) \approx 0.9$ and perturbative validity is lost by $\sim 10^5$~GeV.

hep-ph↗
arXiv2026

Analytical transit light curves for arbitrary power-law limb darkening: a unified framework

We present a unified analytical framework for computing exoplanet transit light curves under arbitrary real power-law limb darkening $I(μ)=I_0μ^α$, $α>-2$, eliminating the two-decade restriction to integer-polynomial forms. Our central result is an exact closed-form expression for the normalised stellar flux in terms of Appell's bivariate hypergeometric function $F_1$, valid for all real $α$ and all geometric transit configurations. Three mutually equivalent formulations -- a geometric kernel representation, a Riemann-Liouville fractional-calculus framework, and a hypergeometric-integrand representation -- provide complementary physical insights and independent computational routes, with inter-method agreement at $|Δ\mathcal{F}|\lesssim 10^{-17}$. The framework encompasses the square-root law ($α=1/2$) essential for M-dwarf characterisation, half-integer powers required by Claret's four-parameter law, and arbitrary real values enabling empirical fitting, while recovering integer-polynomial elliptic-integral expressions as special cases. Validation at 40-digit precision across five geometric regions and eight $α$ values confirms a $\sim10^4\times$ computational speedup over Monte Carlo integration and thirteen orders of magnitude accuracy advantage. Linear superposition enables exact treatment of arbitrary multi-parameter limb-darkening laws without special-case logic.

astro-ph.EP↗
arXiv2026

Grand Unified Origin of Enhanced Scalar Couplings: Connecting Radiative Electroweak Symmetry Breaking to SO(10) Dynamics

We propose that the enhanced Higgs quartic coupling required by radiatively broken electroweak symmetry (RBEWS) emerges naturally from SO(10) grand unification. Our previous analysis demonstrated that a coupling enhancement factor $k = λ_{\rm enhanced}/λ_{\rm SM}$ leads to absolute vacuum stability with a UV Landau pole near the GUT scale for $k \gtrsim 1.03$. The RBEWS prediction $e_{125} = 7.2$ of Steele and Wang, when properly translated from the Coleman-Weinberg scheme at the electroweak VEV to the $\overline{\rm MS}$ scheme at $M_t$ via scheme conversion and scale-dependent ratio evolution, yields $k(M_t) \approx 6.0$--$6.4$, corresponding to a UV pole at $Λ_{\rm UV} \sim {1.5\text{--}2} \times 10^{16}$~GeV -- remarkably close to the GUT scale $M_{\rm GUT} \sim 2 \times 10^{16}$~GeV. We argue this coincidence is not accidental: the UV pole signals the scale where the Standard Model effective description must be embedded into the full SO(10) structure. We derive threshold corrections from SO(10) scalar sectors containing $\mathbf{10}_H$, $\mathbf{\overline{126}}_H$, and $\mathbf{45}_H$ representations, showing that portal couplings between the light Higgs doublet and heavy GUT scalars can generate enhancement factors of order $k \sim 5$--$10$ at the matching scale. The Coleman-Weinberg mechanism operating within a classically scale-invariant GUT scalar potential provides a dynamical origin for both RBEWS and the hierarchy between $M_{\rm GUT}$ and the electroweak scale.

hep-ph↗
arXiv2026

Scale Factorized-Quantum Field Theory: Eliminating renormalization ambiguities in QCD and QED

We introduce Scale Factorized-Quantum Field Theory (SF-QFT), a framework performing path-integral factorization of ultraviolet and infrared momentum modes at a physical scale $Q^*$ before perturbative expansion through Effective Dynamical Renormalization (EDR) with Principle of Observable Effective Matching (POEM) constraints. This yields completely scale and scheme invariant observables. Because the two-loop $β$-function is universal, $a_{\mathrm{eff}}(Q)$ evolves with scheme-independent equations, with higher-order $β$-coefficients absorbed into Wilson coefficients. For the inclusive ratio $R_{e^{+}e^{-}}$, SF-QFT gives $R^{\mathrm{SF-QFT}}(31.6\,\mathrm{GeV}) = 1.05262 \pm 0.0005$, in excellent agreement with experiment ($1.0527 \pm 0.005$) while requiring calculations orders of magnitude simpler than conventional four-loop $\overline{\mathrm{MS}}$ approaches. SF-QFT generates universal algebraic recursion relations producing all higher-order contributions without additional Feynman diagrams. For QED, the formalism yields scheme-independent predictions for the electron anomalous magnetic moment with $a_e^{\text{theory}} = 0.001\,159\,652\,180\,61(76)$, differing from experiment by only $0.15σ$. The framework enables self-consistent extraction of $α_{\text{eff}}^{-1}(m_e) = 137.036005301$. SF-QFT represents a paradigm shift, replacing pursuit of ever-higher loop orders with a unified framework eliminating renormalization ambiguities through systematic EDR and POEM implementation.

hep-ph↗
arXiv2026

Quaternion wavefunction theory bridges quantum formalism and classical fluid dynamics: a zero-parameter derivation of sphere drag

We present a quaternion wavefunction formulation that reduces the incompressible Euler equations to a single nonlinear Schrödinger-type equation with a holomorphic constraint, revealing hidden geometric structure connecting quantum and classical fluid mechanics. The velocity field emerges from a complex quaternion wavefunction $Ψ\in \mathbb{C} \otimes \mathbb{H}$ satisfying a constrained Gross-Pitaevskii equation, with incompressibility enforced through quaternion analyticity conditions that generalize the Cauchy-Riemann equations to three dimensions. This geometric structure provides a selection principle for physically realized Euler solutions, resolving D'Alembert's 270-year-old paradox through geometry rather than phenomenology. The key insight is that incompressibility corresponds to quaternion holomorphicity, known as the Cauchy-Riemann-Fueter conditions, which selects physical solutions from among the infinitely many weak solutions established by De~Lellis and Székelyhidi. Application to steady flow past a sphere yields the Newton regime drag coefficient $C_{D,\infty} = 4/9 \approx 0.44$ as a \textbf{zero-parameter prediction} from quaternion orthogonality constraints, achieving 0.04\% agreement with experiment. This represents the first derivation of this fundamental fluid mechanics constant from first principles. The mechanism parallels how the Kutta condition determines airfoil circulation: quaternion orthogonality constraints break fore-aft pressure symmetry, producing finite drag within inviscid theory.

physics.flu-dyn↗
arXiv2026

BRST Symmetry Violation and Fundamental Limitations of Asymptotic Safety in Quantum Gravity

The asymptotic safety program assumes that quantum gravity becomes renormalizable through ultraviolet fixed points in metric-based couplings. We demonstrate that this approach {encounters fundamental symmetry violations} across multiple independent criteria, all traceable to a single fundamental cause: the breakdown of general covariance and BRST symmetries above the gravitational cutoff scale. Rigorous canonical quantization proves that general covariance cannot be maintained quantum mechanically in dimensions greater than two, while recent path integral calculations reveal persistent gauge parameter dependence in quantum gravitational corrections, signaling BRST symmetry violation. These dual proofs establish that the metric tensor ceases to exist as a valid quantum degree of freedom above $Λ_{\text{grav}}$$\sim$$10^{18}$ GeV, rendering the search for ultraviolet fixed points in metric-based theories {problematic from a foundational physical perspective}. We provide comprehensive analysis demonstrating that asymptotic safety exhibits persistent gauge parameter dependence where fixed-point properties vary with arbitrary gauge choices, non-convergent truncation schemes extending to the 35th order showing no approach to stable values, experimental {tensions} with electroweak precision tests by orders of magnitude, matter content requirements incompatible with the Standard Model, absence of concrete graviton predictions due to gauge and truncation dependence, unitarity {challenges} through ghost instabilities and propagator negativity, and fundamental Wick rotation obstructions preventing reliable connection between Euclidean calculations and physical Lorentzian spacetime. We contrast this with the Unified Standard Model with Emergent Gravity framework that systematically avoids all asymptotic safety pathologies.

gr-qc↗
arXiv2026

Emergent spacetime from spatial energy potentiality: a new theoretical framework for early universe cosmology

We develop a comprehensive cosmological framework based on the principle that our universe originated as a three-dimensional spatial configuration governed purely by energy functionals, with time emerging dynamically through quantum loop corrections. Building on the Unified Standard Model with Emergent Gravity-Effective Field Theory (USMEG-EFT), which provides the first successful unification of quantum gravity with the Standard Model, we demonstrate that spacetime emergence occurs via a first-order phase transition when quantum-generated kinetic terms exceed a critical threshold. This transition naturally resolves the cosmological singularity problem: all curvature invariants remain finite, with $R/M_P^4 \sim 10^{-44}$ and $K/M_P^8 \sim 10^{-88}$ at the critical point. The framework makes definitive, parameter-free predictions for gravitational wave polarizations, exactly two tensor modes confirmed by LIGO-Virgo-KAGRA observations at $>99\%$ confidence, excluding competing approaches that predict additional scalar, vector, or modified polarization content. Post-emergence dynamics naturally implements Starobinsky inflation with spectral index $n_s = 0.964$ and tensor-to-scalar ratio $r = 0.004$, in excellent agreement with Planck constraints. The phase transition dynamics generate enhanced primordial non-Gaussianity $f_{\rm NL}^{\rm local} \in [0.8, 2.5]$, testable with CMB-S4 (projected $σ\sim 1$), and a stochastic gravitational wave background peaking in the LISA sensitivity band ($f \sim 10^{-4}$ Hz, $Ω_{\rm GW}h^2 \sim 10^{-6}$). The framework naturally addresses the Hubble tension through scale-dependent modifications to cosmic expansion arising from residual phase transition effects.

physics.gen-ph↗
arXiv2025

Is methane the 'climate culprit'? The dangers of using imprecise, long-term GWP for methane to address the climate emergency

The United Nations Environmental Program's (UNEP) Emissions Gap Report, 2023, Temperatures hit new highs, yet world fails to cut emissions (again)'', and in 2024, No more hot air, emissions' massive gap between rhetoric and reality''. A climate emergency has been declared yet policies and emission reductions continue to fail. Global temperature anomalies in recent years have not been modelled well. Methane (CH4) is a potent greenhouse gas (GHG) with a short atmospheric half-life (~8.4 years), and a perturbation lifetime of 11.8 $\pm$ 1.8 yrs (IPCC AR6). It has a high, short-term impact on global warming: substantially greater than CO2. Traditional metrics such as the 100-year Global Warming Potential (GWP100) obscure the short-term, negative climatic effects of CH4, potentially leading to inadequate policy responses. This study examines the limitations of GWP100 in capturing the true, immediate climate impact of CH4 and its inability to incorporate varying emissions, explores alternative metrics, and discusses the multi-faceted implications of this under-reporting of CH4 emissions. Recalculation of 2024 Emissions Gap Report using a ten-year GWP of 105 increased CH4's warming effect to almost 90% of CO2, rather than 25% using a GWP100 of 28. We highlight the necessity of adopting a more immediate time horizon for CH4's warming effects, accelerating climate emergency action, while recognizing the adverse effects of the rapid growth rate of CH4 emissions on reduction efforts. To overcome the limitations of GWP100, a static constant, we propose GWPEFF(t) which dynamically represents warming across various time periods. It is a novel, physically realistic measure that is simple to understand, and effective for policies in reducing short-term emissions such as CH4.

physics.ao-ph↗
arXiv2025

Restricting One-Loop radiative effects in quantum gravity: Demonstrating 4D GR as an EFT and its consistent unification with the Standard Model

In ``On restricting to one-loop order the radiative effects in quantum gravity" (Brandt, Frenkel, and McKeon, 2020) \cite{Brandt2020}, a Lagrange multiplier (LM) field is introduced into the Einstein-Hilbert action, removing all multi-loop graviton diagrams and confining quantum-gravity corrections to just one loop. The resulting one-loop effective action carries a term proportional to {$\ln(μ/Λ)$}, which they suggest could be experimentally determined, hinting at direct measurements of quantum-gravity effects. We {demonstrate}, however, that {$μ$ and $Λ$} emerge from a chosen renormalization scheme, not from physical observables, implying that {$\ln(μ/Λ)$} signals a finite UV cutoff in this ``LM renormalization scheme.'' Although Newton's constant remains fixed (no running of {$G_N$}), the resulting logarithmic dependence encodes a limited domain of validity for General Relativity (GR) in four dimensions, thereby demonstrating explicitly that 4D GR behaves as an effective field theory (EFT) for energies below the cutoff. {Using the Appelquist-Carazzone decoupling theorem, we prove mathematically that this framework has a well-defined low-energy limit.} We then illustrate how this truncated, renormalized gravity sector can be consistently unified with the Standard Model (SM), yielding a finite and renormalized EFT encompassing both gravity and particle physics up to a scale {$Λ_{\text{grav}}$}. As such, we term this unification as the USMEG-EFT (Unified Standard Model with Emergent Gravity-EFT) framework. Our work represents a breakthrough in theoretical physics with a first successful unification of gravity with the Standard Model through a fully renormalizable and EFT framework.

hep-th↗
arXiv2025

A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications

We present a novel, unified quaternion-complex framework for formulating the incompressible Navier-Stokes equations that reveals the geometric structure underlying viscous fluid motion and resolves the Clay Institute's Millennium Prize problem. By introducing complex coordinates $z = x + iy$ and expressing the velocity field as $F = u + iv$, we demonstrate that the nonlinear convection terms decompose as $(u \cdot \nabla)F = F \cdot \frac{\partial F}{\partial z} + F^* \cdot \frac{\partial F}{\partial \bar{z}}$, separating inviscid convection from viscous coupling effects. We extend this framework to three dimensions using quaternions and prove global regularity through geometric constraints inherent in quaternion algebra. The incompressibility constraint naturally emerges as a requirement that $\frac{\partial F}{\partial z}$ be purely imaginary, linking fluid mechanics to complex analysis fundamentally. Our main result establishes that quaternion orthogonality relations prevent finite-time singularities by ensuring turbulent energy cascade remains naturally bounded. The quaternion-complex formulation demonstrates that turbulence represents breakdown of quaternion-analyticity while maintaining geometric stability, providing rigorous mathematical foundation for understanding why real fluids exhibit finite turbulent behavior rather than mathematical singularities. We prove that for any smooth initial data, there exists a unique global smooth solution to the three-dimensional incompressible Navier-Stokes equations, directly resolving the Clay Institute challenge. Applications to atmospheric boundary layer physics demonstrate immediate practical relevance for environmental modeling, weather prediction, and climate modeling.

physics.flu-dyn↗
arXiv2024

Advancing Heatwave Forecasting via Distribution Informed-Graph Neural Networks (DI-GNNs): Integrating Extreme Value Theory with GNNs

Heatwaves, prolonged periods of extreme heat, have intensified in frequency and severity due to climate change, posing substantial risks to public health, ecosystems, and infrastructure. Despite advancements in Machine Learning (ML) modeling, accurate heatwave forecasting at weather scales (1--15 days) remains challenging due to the non-linear interactions between atmospheric drivers and the rarity of these extreme events. Traditional models relying on heuristic feature engineering often fail to generalize across diverse climates and capture the complexities of heatwave dynamics. This study introduces the Distribution-Informed Graph Neural Network (DI-GNN), a novel framework that integrates principles from Extreme Value Theory (EVT) into the graph neural network architecture. DI-GNN incorporates Generalized Pareto Distribution (GPD)-derived descriptors into the feature space, adjacency matrix, and loss function to enhance its sensitivity to rare heatwave occurrences. By prioritizing the tails of climatic distributions, DI-GNN addresses the limitations of existing methods, particularly in imbalanced datasets where traditional metrics like accuracy are misleading. Empirical evaluations using weather station data from British Columbia, Canada, demonstrate the superior performance of DI-GNN compared to baseline models. DI-GNN achieved significant improvements in balanced accuracy, recall, and precision, with high AUC and average precision scores, reflecting its robustness in distinguishing heatwave events.

cs.LG↗
arXiv2023

On the breakdown of space-time in general relativity

Based on the canonical quantization of $d>2$ dimensional general relativity (GR) via the Dirac constraint formalism (also termed as `constraint quantization'), we propose the loss of covariance as a fundamental property of the theory. This breakdown occurs for the first-order Einstein Hilbert action, whereby loss of diffeomorphism invariance, besides first class constraints, second class constriants also exist leading to non-standard ghost fields which render the path integral non-covariant. We also attempt, for the first time, the canonical quantization via calculation of the path integral for the equivalent Hamiltonian formulation of GR for which only first class constraints exist. However, loss of covariance still occurs in this action due to loss of diffeomorphism invariance and structures arising from non-covariant constraints in the path integral. In contrast, we find that covariance as a symmetry is restored and quantization with perturbative calculations is possible in the weak limit of the gravitational field of these actions. Hence, we firstly establish, for the first time, that the breakdown in space-time is a property of GR itself as its limitation, indicating it to be an Effective Field Theory (EFT). We further propose that the breakdown of space-time occurs as a non-perturbative feature of GR in the strong field limit of the theory. Besides GR, we also note that covariance is preserved when constraint quantization is conducted for non-Abelian gauge theories, such as the Yang-Mills theory. These findings are novel from a canonical gravity formalism and EFT approach, and are consistent with GR singularity theorems, yet are general and extend them, as the singularity theorems indicate breakdown at a strong field limit of GR in black holes.

gr-qc↗
arXiv2022

Achieving effective renormalization scale and scheme independence via the Principle of Observable Effective Matching

In this work, we explicate a new approach for eliminating renormalization scale and scheme (RSS) dependence in observables. We develop this approach by matching RSS dependent observables (such as cross-sections and decay rates) to a theory which is independent of both these forms of dependencies. We term the fundamental basis behind this approach as the principle of observable effective matching (POEM), which entails matching of a scale- and scheme-dependent observable with the fully physical scale (PS) and dynamical scale-dependent theory at loop orders at which RSS independence is guaranteed. This is aimed toward achieving so-called "effective" RSS-independent expressions as the resulting dynamical dependence is derived from a particular order in RSS-dependent perturbation theory. With this matching at a PS at which the coupling (and masses) is experimentally determined at this scale, we obtain an "effective theoretical observable (ETO)", a finite-order RSS-independent version of the RSS-dependent observable. We illustrate our approach with a study of the cross-section ratio $R_{e^{+}e^{-}}$ for $e^{+}e^{-}\rightarrow$ hadrons, which is demonstrated to achieve scale and scheme independence utilizing the three- and four-loop order MS scheme expression in QCD perturbation theory via matching at both one-loop and two-loop orders for obtaining the ETO. With two-loop matching, we obtain an ETO prediction of $\frac{3}{11}R_{e^{+}e^{-}}^{eff}=1.052431_{-0.0006}^{+0.0006}$ at $Q=31.6 GeV$, which is in excellent agreement with the experimental value of $\frac{3}{11}R_{e^{+}e^{-}}^{exp}=1.0527_{-0.005}^{+0.005}$.

hep-ph↗