It is well known that a strictly massless spin-3/2 particle can interact consistently only within supergravity. Recently, positivity arguments have shown that an effective field theory of a massive Majorana spin-3/2 particle admits an arbitrarily small mass only if a graviton is present and the four-fermion contact interactions are tuned to the values dictated by $$ \mathcal{N} $$ = 1 supergravity. In this work, we investigate how this limit is approached at finite mass. Assuming that the graviton $\textit{t}$-channel pole can be discarded, we derive non-forward, tree-level dispersive bounds on massive spin-3/2 contact operators and determine the region of effective couplings consistent with unitarity and analyticity. For sufficiently small $\textit{m}$, we find that the allowed parameter space forms a bounded, Planck-suppressed neighbourhood of the supergravity point, defined by the supergravity values of the four-fermion couplings. The supergravity point lies on the boundary of this region. In the regime $\textit{m}$ ≪ $\textit{M}$ , the volume of the allowed region scales parametrically as

India

Jay Desai

Diptimoy Ghosh

China

Saurabh Pant

Positivity in massive spin-3/2 EFTs and the Planck-suppressed neighbourhood of supergravity

We formulate a unified theoretical framework for the fractional dynamics of graphene Dirac quasiparticles within the Riemann-Liouville (RL) fractional calculus approach. In this case, by starting from the fractional graphene Dirac equation, we derive an exact hydrodynamic formulation through the systematic construction of the density, current, and pseudospin evolution equations without applying perturbative assumptions or phenomenological approximations. Moreover, the fractional relativistic Langevin description is subsequently established to incorporate stochastic contributions into the relativistic hydrodynamic dynamics, allowing a consistent treatment of fluctuations in fractional quantum systems. Within this formulation, the corresponding fractional Fokker-Planck equation and relativistic stochastic Hamilton-Jacobi equation are derived, providing a complete statistical framework for analyzing fractional quantum transport processes. Also, the resulting hydrodynamic variables are then used to reconstruct the fractional graphene Dirac equation exactly, confirming the equivalence between the original spinor representation and the hydrodynamic description at the mathematical level. Furthermore, we introduce a fractional geometric hydrodynamic reconstruction operator and extend the developed formalism to curved spacetime in the RL framework, leading to a covariant description of fractional graphene dynamics in nontrivial geometries. In this context, this formulation provides a systematic theoretical structure connecting fractional relativistic quantum dynamics, stochastic transport mechanisms, and geometric hydrodynamic methods, enabling the investigation of nonlocal transport behavior and anomalous diffusion effects in graphene and other Dirac materials.

Azerbaijan

Algeria

Abdelmalek Bouzenada

Thailand

Czechia

Rami Ahmad El-Nabulsi

Brazil

Allan R.P. Moreira

Fractional stochastic hydrodynamics and Fokker-Planck dynamics of <math altimg='si1.svg'><mrow><mn>2</mn><mi mathvariant='script'>D</mi></mrow></math> graphene Dirac quasiparticle models

Charged massive spin-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></math> fields have long been regarded as problematic, because their coupling to electromagnetism generically leads to loss of hyperbolicity, acausal propagation and loss of unitarity. At the same time, fractionally charged supermassive gravitinos play a central role in a recent proposal of two of the present authors, where they are the only fermionic degrees of freedom beyond the Standard Model and provide novel dark matter candidates. We address this apparent tension by revisiting the result of Deser and Waldron, who showed that the inclusion of gravity can compensate the electromagnetic source of the inconsistency. For a minimally coupled Rarita-Schwinger field in an Einstein-Maxwell background, consistency requires a lower bound on the mass in terms of the charge and the cosmological constant. What is usually a severe obstruction to low-energy charged spin-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></math> phenomenology becomes an independent indication that such particles must lie close to the Planck scale, as argued by two of the present authors on other grounds. We rederive the inequality from the solvability of the Rarita-Schwinger constraints and from the characteristic determinant, emphasizing how the Einstein-Maxwell stress tensor compensates the purely electromagnetic pathology. We then reformulate the system using a Stückelberg spinor, showing that the helicity-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math> sector reproduces the same condition. This formulation is also essential for obtaining a renormalizable propagator. We discuss this propagator and the corresponding ghost system.

Poland

Artur Krawczyk

Krzysztof A. Meissner

Germany

Hermann Nicolai

Bartłomiej Sikorski

Planck mass gravitinos in Einstein-Maxwell backgrounds

Classically scale-invariant (and perturbative) theories provide a way to understand large hierarchies, as scales are generated through dimensional transmutation. They always lead to first-order phase transitions, since symmetries are radiatively broken, and they generically feature quasiflat potentials, which are suitable for inflation. We construct a simple but fully realistic model of this kind that accounts for all observational evidence of new physics and is remarkably compatible with the most recent constraints on inflationary observables from both the Planck/BICEP/Keck and the Atacama Cosmology Telescope Collaborations. This model illustrates how classical scale invariance generically leads to a nonstandard cosmology in which inflation occurs in two stages: a slow-roll stage and a thermal stage, separated by a radiation-dominated era.

Italy

Filippo Cutrona

Francesco Rescigno

Alberto Salvio

ACT-Planck data and phase transitions from a viable no-scale Standard Model completion

We examine the impact on the phenomenology of the minimal supersymmetric SU(5) Grand Unified Theory (GUT) of dimension-5 operators with coefficients suppressed by the Planck mass scale, with particular emphasis on predictions for nucleon decay. We incorporate dimension-5 operators in both the Higgs sector and the Yukawa interactions in the theory, and take account of the constraints from gauge coupling measurements, the mass of the Higgs boson, fermion masses and the cold dark matter density. We consider two scenarios for soft supersymmetry breaking: the constrained minimal supersymmetric extension of the Standard Model (CMSSM) and the Non-Universal Higgs Model (NUHM). We present predictions for the nucleon decay modes $$p \rightarrow \pi ^0 e^+, \pi ^0 \mu ^+, K^+ \bar{\nu }, \pi ^+ \bar{\nu }$$ , $$K^0 e^+, K^0 \mu ^+$$ and $$n\rightarrow \pi ^0 \bar{\nu }$$ , $$\pi ^- e^+, K^0 \bar{\nu }$$ , which we compare with both the present experimental sensitivities and those projected for the JUNO and Hyper-Kamiokande experiments. We find that these experiments may have interesting possibilities for discovering several of these decay modes.

Estonia

United Kingdom

Switzerland

John Ellis

United States

Jason Evans

Shihwen Hor

Japan

Natsumi Nagata

Keith Olive

Planck-scale effects on nucleon decay in minimal supersymmetric SU(5)

We develop a framework for testing quantum gravity through the stochastic gravitational-wave background produced by evaporating near-Planck-mass primordial black holes. Because gravitons freestream from the emission region without rescattering, they preserve a direct spectral record of the black-hole temperature–mass relation <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mo stretchy="false">(</mo><mi>M</mi><mo stretchy="false">)</mo></math>, a relation that is erased for all other Hawking-radiated species by rapid thermalization. We translate six representative phenomenological beyond-semiclassical frameworks (the generalized uncertainty principle, loop quantum gravity, noncommutative geometry, asymptotic safety, string/Hagedorn physics, and tunneling backreaction) into distinct <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mo stretchy="false">(</mo><mi>M</mi><mo stretchy="false">)</mo></math> parameterizations and compute the resulting gravitational-wave spectra numerically within a hybrid semiclassical-phenomenological framework. Modifications that suppress <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>T</mi><mo stretchy="false">(</mo><mi>M</mi><mo stretchy="false">)</mo></mrow></math> shift the spectral peak by up to 10 decades in frequency, in some cases into the sensitivity bands of next-generation interferometers or resonant-cavity detectors, while models imposing a hard evaporation cutoff produce distinctive peak morphologies that distinguish between phenomenological classes of modified evaporation. We further discuss the impact of different choices for post-inflationary conditions in the very early Universe and note that breaking the remaining cosmological degeneracies and connecting these signatures to specific quantum-gravity theories requires complementary observables. We find that the relative spectral displacement between the standard Hawking prediction and any modified model is cosmology-independent, and hence spectral shape rather than absolute peak frequency provides the cleanest probe of Planck-scale physics.

Stefano Profumo

Probing Planck-scale physics with high-frequency gravitational waves

Determining whether Planck-scale effects can stabilize black holes addresses fundamental questions about black hole evaporation and quantum gravity consistency. Here, we analyze the thermodynamic topology ofSchwarzschild black holes under Planck-scale modified kinematics, using a cubic entropy correction derived from a well-known phenomenological MDR with leading correction $$\eta E^3/E_P$$ . Enforcing physical constraints ( $$S'(r_h) > 0$$ , $$T > 0$$ ) via the entropy-geometry correspondence, we find a single unstable branch with $$w = -1$$ and $$W = -1$$ for both signs of the correction parameter. A second root suggesting stability ( $$w = +1$$ ) is excluded due to negative mass/temperature and lies outside the perturbative regime. Thus, this class of MDRs does not yield stable Schwarzschild black holes. However, MDRs with different leading-order corrections may behave otherwise, leaving the search for Planck-scale stabilization an open endeavor.

Iran

Mohsen Khodadi

Kazakhstan

Nosratolla Jafari

Shahin Mamedov

A winding number analysis of Schwarzschild black hole stability in light of Planck-scale modified kinematics

We consider a Universe with a three-torus topology, which before inflation is devoid of any matter or radiation. Its preinflationary evolution is driven solely by Casimir energies of the existing fields, with a radiationlike equation of state. We show that, under natural assumptions and with the appropriate number of fermions and bosons in the theory, such a Universe can start its evolution from a Planck size at the Planck time. Moreover, assuming typical parameters for inflation and reheating, the three-torus Universe can be several Hubble radii across at present time, which is precisely the size hinted by the anomaly in the cosmic microwave background observed at low multipole moments. We derive a relation between the size of the Universe, the number of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>e</mi></mrow></math>-folds of inflation, and the energy density decrease during reheating, which we then use to determine the parameter values consistent with the anomaly and the lower bound on the size of the Universe from the Planck satellite.

Bartosz Fornal

Universe originating from an empty Planck-size torus

In this paper, a generalized Dunkl-Fokker-Planck equation in <math altimg='si1.svg'><mrow><mo>(</mo><mn>1</mn><mo linebreak='goodbreak'>+</mo><mn>1</mn><mo>)</mo></mrow></math> dimensions is formulated within a fractional calculus setting based on the Riemann-Liouville (RL) derivative. In this case, the construction employs reflection-deformed operators to represent parity-dependent structures together with nonlocal memory contributions characteristic of fractional evolution. Also, the associated Wigner-Dunkl supersymmetric (SUSY) framework is developed, providing a consistent algebraic structure that extends standard supersymmetry under fractional dynamics. Moreover, the system is examined for a harmonic oscillator potential combined with a centrifugal-type interaction, where the coupling between Dunkl deformation and fractional order produces modified dynamical behavior and effective transport properties. By applying an exact Foldy-Wouthuysen (FW) transformation, a nonlocal relativistic operator form of the system is obtained, yielding a closed fractional Dunkl structure governed by RL dynamics. In addition, a higher-order Foldy-Wouthuysen reduction is used to derive effective Dunkl-Fokker-Planck evolution equations from reflection-deformed relativistic quantum systems. In this context, the resulting formulation establishes a unified description of fractional diffusion, relativistic corrections, and Dunkl symmetry within an operator-based framework, with applications to generalized quantum transport and deformed statistical systems.

Fractional Dunkl-Fokker-Planck operators in supersymmetric (SUSY) quantum state under Foldy-Wouthuysen (FW) transformation

Employing the generalized free energy landscape and solving the associated Fokker–Planck equation, we obtain the time-dependent probability evolution of the order parameter for the RN-AdS black hole phase transitions. Our analysis reveals two distinct kinetic regimes, namely relaxation dynamics initialized at the unstable maximum and phase transition from the metastable state. Furthermore, we characterize the non-equilibrium irreversibility and macroscopic uncertainty using the entropy production rate and the Shannon entropy. The results demonstrate that the phase transition synchronizes exactly with a prominent peak in the entropy production rate, identifying the barrier crossing event as a process fundamentally driven by maximum thermodynamic dissipation.

Chao Wang

Chen Ma

Meng-Ci He

Bin Wu

Probabilistic evolution of black hole thermodynamic states via Fokker–Planck equation