Muzaffer Adak - The Generalized Dirac Equation in the Metric Affine Spacetime
Pamukkale University, Department of Physics
Abstract: We discuss the most general form of the Dirac equation in metric-affine spacetimes containing curvature, torsion, and non-metricity. It incorporates all bases of the Clifford algebra within the spinor connection. In an orthonormal basis, the dynamics of the geometry is governed by the coframe and the affine connection, without an explicit metric component. Accordingly, we consider all possible combinations of the coframe, the affine connection 1-form, and the bases of the Clifford algebra in the orthonormal frame.
As a consistency cross-check, we adopt two approaches. First, the generalized Dirac equation is formulated directly by applying the minimal coupling prescription to the original Dirac equation. Second, after applying the minimal coupling prescription to the original Dirac Lagrangian, the generalized Dirac equation is derived via a variational procedure. Requiring the equivalence of these two results leads to novel constraints on the arbitrary coupling constants appearing in the covariant derivative of the spinor.
A detailed analysis of the group structure generated by the new terms appearing in the generalized covariant derivative of the spinor is left for future work.
References:
[1] M. Adak, et al., "The Generalized Dirac Equation in the Metric Affine Spacetime", arXiv:2506.23609.
Özgür Akarsu - Toward Theoretical Realizations of ΛsCDM Cosmology and Their Implications for Cosmological Tensions
Istanbul Technical University, Department of Physics Engineering
Abstract: The remarkable phenomenological success of the concordance ΛCDM model is accompanied by a growing set of tensions and anomalies, including those associated with H0, S8, the growth index γ, and neutrino-mass inference, which may be hinting at missing structure in the standard cosmological framework. In this talk, I will discuss the ΛsCDM cosmology, a sign-switching cosmological-constant scenario in which the effective dark-energy sector undergoes a late-time AdS-to-dS(-like) transition. The main emphasis will be on the question of theoretical realization: namely, how such a transition may arise from a more fundamental description rather than being regarded as a purely phenomenological construction. I will review representative mechanisms and theoretical settings in which ΛsCDM-like dynamics can emerge, and discuss the physical interpretation of a late-time transition from an effectively negative to a positive vacuum-energy contribution. I will then briefly comment on recent observational and theoretical developments suggesting that this framework may provide a minimal yet structurally novel extension of ΛCDM, capable of improving the consistency among distinct cosmological probes while pointing toward a revised concordance picture.
Emel Altaş - Love in de Sitter Spacetime
Abdullah Gül University, Department of Engineering Science
Abstract: After the detection of gravitational waves, interest in observable quantities measurable by gravitational wave detectors has significantly increased. Recent studies have shown that during the inspiral phase of a binary collapse, a dimensionless quantity known as the Love number—which characterizes the response of a gravitating body to an external tidal field—can be measured. This finding opens the possibility of probing modified gravity theories and constraining the equation of state of neutron stars. By expanding the first-order metric perturbations in terms of scalar, vector, and tensor spherical harmonics, we constructed the Love numbers that describe how a gravitating body responds to an external companion.
References:
[1] Emel Altas, Ercan Kilicarslan, Onur Oktay, Bayram Tekin, "Static Tidal Perturbations of Relativistic Stars: Corrected Center Expansion and Love Numbers-I", arXiv:2604.15195v1 [gr-qc], TUBITAK grant no: 123F353.
Ekrem Aydıner - A Possible Solution to Six Fundamental Problems in Cosmology
Istanbul University, Department of Physics
Abstract: The ΛCDM model, considered the standard model of modern cosmology, is consistent with data from observations of cosmic microwave background radiation, galaxy distributions, and supernovae. However, the ΛCDM model does not answer many fundamental questions in cosmology.
Some of the most widely discussed problems [1-7] include: 1) the initial singularity problem, 2) the physical origin of the transition from a matter-dominated era to a dark-energy-dominated era, 3) the cosmic coincidence problem, 4) the lack of a unified analytical scale factor describing the full cosmic evolution, 5) the Hubble tension, and 6) the cosmological conditions and timing associated with the emergence of life.
There are numerous studies, models, and theories in the literature to solve these problems. However, so far, no model or theory has yet been proposed that solves these problems with complete certainty.
In this talk, I will first briefly address these six fundamental problems in cosmology. Next, based on the model [3] we proposed in 2022 for the interaction of dark matter and dark energy, I will show, within the framework of my new analyses [1, 7], that these six fundamental problems of physical cosmology can be solved.
The results show that the dark matter-dark energy interaction model offers a consistent and unified dynamic framework that can explain fundamental problems of cosmology [4, 5]. However, this structure points to the fact that interacting systems can be inherently chaotic, and in this respect, it exhibits a natural compatibility with Chaotic Universe Theory [6, 7].
References:
[1] E. Aydiner, "A Possible Solution to Six Fundamental Problems in Cosmology" (2026) -submitted-.
[2] E. Aydiner, E. "Matter, Dark Matter, Dark Energy Interactions and New Physics" In: Aydiner, E., Sidharth, B.G., Michelini, M., Corda, C. (eds) Frontiers of Fundamental Physics FFP16. (2022) Springer Proceedings in Physics, vol 392. Springer, Cham. https://doi.org/10.1007/978-3-031-38477-6_2.
[3] E. Aydiner et al. "Late Time Transition of Universe and the Hybrid Scale Factor" Eur. Phys. J. C 82, 39 (2022). https://doi.org/10.1140/epjc/s10052-022-09996-2.
[4] E. Aydiner, "Chaotic Interaction Between Dark Matter and Dark Energy" Int. J. Theor. Phys. Vol: 64, p.3 (2025). https://doi.org/10.1007/s10773-024-05871-w.
[5] E. Aydiner, "Chaotic Interaction Between Thermodynamic Systems" Annals of Physics. Vol: 480, p.170079 (2025). https://doi.org/10.1016/j.aop.2025.170079.
[6] E. Aydiner, "Chaotic Universe Model" Sci. Rep. 8, 721 (2018). https://doi.org/10.1038/s41598-017-18681-4.
[7] E. Aydiner, "Chaotic Universe Theory: A short review and discussion" (2026) -submitted-.
Cemsinan Deliduman - f(R) Gravity in an Ellipsoidal Universe
Mimar Sinan Fine Arts University, Department of Physics
Abstract: A new model of cosmology, the γδCDM model, is proposed based on an anisotropic background and a specific f(R) theory of gravity. This model is distinguished in two important aspects from the ΛCDM model: firstly, the contribution of different energy densities to the Hubble parameter are weighted with different weights, and then, dependence of energy densities to redshift is modified as well. This unorthodox relation of energy content to the Hubble parameter brings forth a new way of interpreting the cosmological history. This model does not allow the existence of a cosmological constant component; nonetheless, a redshift-dependent dark energy contribution is possible. We tested observational relevance of the new model by best fitting to different data sets. It will be presented that that this model could accommodate the idea of cosmological coupling of black holes. It could also bring an explanation to the “impossibly early galaxy problem” by allocating more time for the observed large and massive structures to form from the initial seeds. Thanks to a modified time-redshift relation, the γδCDM model has a more plausible time period at high redshift for large and massive galaxies and massive quasars to form, whereas the age of the Universe today is not modified significantly. We will also show that the Hubble constant is a true constant in this model, it does not evolve with redshift, unlike in the case of the ΛCDM model. The value of the Hubble constant obtained in the γδCDM model is in the 1σ bound of the late Universe observations.
References:
[1] C. Deliduman, O. Kasikci and V. K. Tugyanoglu, "f(R) Gravity in an Ellipsoidal Universe", Phys. Dark Univ. 44, 101469 (2024), doi:10.1016/j.dark.2024.101469, [arXiv:2310.02914 [gr-qc]].
[2] S. S. Binici, C. Deliduman and F. Ş. Dilsiz, "The Ages of the Oldest Astrophysical Objects in an Ellipsoidal Universe", Phys. Dark Univ. 46, 101600 (2024), doi:10.1016/j.dark.2024.101600, [arXiv:2402.16646 [astro-ph.CO]].
[3] F. Ş. Dilsiz, C. Deliduman and S. S. Binici, "Testing γδCDM Model in the Redshift Bins", Phys. Dark Univ. 48, 101943 (2025), doi:10.1016/j.dark.2025.101943, [arXiv:2501.07538 [astro-ph.CO]].
[4] C. Deliduman, F. Ş. Dilsiz and S. S. Binici, "Growth Index in the γδCDM Model", Phys. Dark Univ. 51, 102201 (2026), doi:10.1016/j.dark.2025.102201, [arXiv:2508.14749 [astro-ph.CO]].
Mahmut Elbistan - Hidden Symmetries of Exact Plane Gravitational Waves and the Eisenhart-Duval Lift
Bilgi University, Department of Energy System Engineering
Abstract: Isometries and conformal symmetries of spacetime metrics are generated by Killing vectors and the related charges can be built via Noether's theorem. Hidden symmetries, on the other hand, are associated with higher rank Killing tensors and they do not simply follow from the Noether's theorem. In this talk, I will discuss the Killing tensors of exact plane GWs which can be obtained from the Pais-Uhlenbeck oscillator via Eisenhart-Duval lift.
Oğul Esen - Geometric Hamilton-Jacobi Theory: From Fundamentals to Non-Equilibrium Thermodynamics and Implicit Dynamics
Gebze Technical University, Department of Mathematics
Abstract: This talk focuses on geometric Hamilton--Jacobi theory. It is organized in three parts. We begin with a brief overview of its main ideas and geometric framework. We then show how irreversible thermodynamics, in particular the GENERIC formalism (General Equation for Non-Equilibrium Reversible--Irreversible Coupling), can be realized within the setting of geometric Hamilton--Jacobi theory. We conclude by discussing an extension of geometric Hamilton--Jacobi theory to implicit dynamics and illustrate the approach with an example from nonholonomic dynamics.
Yaghoub Heydarzade - FLRW-Cosmology in Scalar-Vector-Tensor Theories of Gravity
Bilkent University, Department of Mathematics
Abstract: We generalize our previous theorem for FLRW spacetimes within the framework of generic metric gravity theories. In earlier work, we proved that, in the absence of matter fields, the field equations of any metric gravity theory constructed from the curvature tensor and its covariant derivatives reduce in FLRW spacetime to the Einstein equations with an effective perfect-fluid source. In the present work, we extend this result to a broad class of scalar-vector-tensor theories in which the gravitational action contains arbitrary scalar and vector fields together with their covariant derivatives at any order. We prove that, under the symmetry conditions imposed by FLRW geometry, the metric field equations necessarily take the Einstein form with an effective perfect-fluid source, supplemented by the corresponding scalar and vector field equations. This result shows that FLRW metrics belong to the class of universal metrics: the tensorial structure of the gravitational field equations is solely fixed by the symmetry of the FLRW spacetime and is independent of the specific form of the gravitation theory, while the resulting cosmological dynamics remains theory dependent. We illustrate our theorem using recently proposed Einstein-scalar and Einstein-Proca theories.
References:
[1] M. Gürses, Y. Heydarzade, "FLRW-Cosmology in Scalar-Vector-Tensor Theories of Gravity", arXiv:2602.14808.
[2] M. Gürses, Y. Heydarzade, "FLRW-Cosmology in Generic Gravity Theories", Eur. Phys. J. C 80, 1061 (2020).
[3] M. Gürses, Y. Heydarzade, Ç. Şentürk, "Geometric Perfect Fluids and Dark Side of the Universe", Phys. Rev. D 110, 024073 (2024).
Sercan Kaya - Can Fractional Time Operators Reproduce Gravitational-Wave Memory?
Middle East Technical University, Department of Physics
Abstract: We initiate an investigation into whether fractional calculus, with its intrinsic long-tailed memory and nonlocal features, can provide a viable model for gravitational-wave memory effects. We consider two toy constructions: (i) a fractional modification of the linearized Einstein field equations using a sequential Caputo operator; and (ii) a fractionalized quadrupole formula in which the same operator acts on the source moment. Both constructions yield history-dependent responses with small memory-like offsets. However, in all cases we studied, the signal decays to zero at late times, failing to reproduce the permanent displacement predicted by General Relativity. We showed that, under asymptotic and spatial flatness of spacetime, the solutions of the proposed models decay to zero at late times when the time derivatives of the perturbed metric are temporally localized and bounded at each spatial point. Therefore, our results constitute a no-go demonstration: naive fractionalization is insufficient to model the permanent offset in the metric without explicitly building in flux-balance laws or asymptotic symmetry structure. We argue that any successful model must incorporate fractional kernels directly into the hereditary flux-balance integral of General Relativity while preserving gauge invariance and dimensional consistency. We also discuss possible connections to modified gravity and the absence of memory in spacetime with dimensions greater than four dimensions.
Reference:
S. Kaya, B. Tekin "Can Fractional Time Operators Reproduce Gravitational-Wave Memory? A No-Go Result", (2026) arXiv:2510.07232.
Sylvain Lavau - Supersymmetric Poisson and Poisson-supersymmetric Sigma Models
Galatasaray University - Department of Mathematics
Abstract: We revisit and construct new examples of supersymmetric 2D topological sigma models whose target space is a Poisson supermanifold. Inspired by the AKSZ construction of topological field theories, we follow a graded-geometric approach and identify two commuting homological vector fields compatible with the graded symplectic structure, which control the gauge symmetries and the supersymmetries of the sigma models. Our analysis unifies Jackiw-Teitelboim supergravity and differential Poisson sigma-models exhibiting de Rham supersymmetry and reveals the existence of new models in the same family. Two distinguished cases exist: the differential Poisson sigma model constructed before by Arias, Boulanger, Sundell and Torres-Gomez and the other a contravariant differential Poisson sigma model.
Joint work with T. Basile, A. Chatzistavrakidis and A. Hrelja.
Ali Mostafazadeh - A Class of Exactly Solvable Diffraction-Grating Scattering Problems
Koç University, Department of Physics and Mathematics
Abstract: In [1], Berry uses the Raman-Nath formalism for treating diffraction gratings [2, 3] to prove the exact solvability of the problem of computing the diffracted beam intensities for atoms incident upon a grating given by the interaction potential,
v(x, y) := { iV0(ei k y - 1) for 0 < x < ℓ ; 0 otherwise
where V0, k, and ℓ are positive real parameters. His results, which rely on paraxial approximation and are valid for sufficiently small incidence angles, also apply to the diffraction of TE waves by a nonmagnetic optical grating with a relative permittivity of the form ε(x, y) := 1—v(x, y)/k2, where k is the wavenumber of the incident wave. We have recently developed a dynamical formulation of the stationary scattering defined by Bergmann’s equation in two dimensions which describes the scattering of TE and TM waves incident up on a general (possibly magnetic) two-dimensional material as well as acoustic scattering in two dimensions [4]. This is an approach to scattering theory in which one maps the scattering problem to the quantum dynamics generated by an effective non-Hermitian Hamiltonian operator. We use it to identify a large class of exactly solvable diffraction gratings which includes Berry’s grating. We outline an essentially algebraic method for computing the exact values of the diffracted beam intensities for both TE and TM waves scattered by gratings belonging to this class.
References:
[1] M. V. Berry, "Lop-sided Diffraction by Absorbing Crystals", J. Phys. A 31, 3493-3502 (1998).
[2] C. V. Raman and N. S. N Nath, "The Diffraction of Light by High Frequency Sound Waves: Part IV, Generalised Theory", Proc. Indian Acad. Sci. A 3, 119-25 (1936).
[3] M. V. Berry, "The Diffraction of Light by Ultrasound" (Academic Press, London, 1966).
[4] F. Loran and A. Mostafazadeh, "Scattering of TE and TM Waves by Inhomogeneities of a 2D Material, Low-frequency Behavior of the Scattering Amplitude, and Low-frequency Invisibility", to appear in Prog. Theor. Exp. Phys. (2026).
Mustafa Mullahasanoğlu - Integrability from Duality and Duality from Integrability
Boğaziçi University, Department of Physics
Abstract: This talk reviews recent progress in constructing novel integrable lattice spin models through the gauge/Yang–Baxter correspondence, a powerful framework linking supersymmetric gauge theories to exactly solvable models in statistical mechanics. I will begin by summarizing how duality properties of three-dimensional supersymmetric gauge theories yield new solutions to the star–triangle and star–star relations, the fundamental integrability conditions for two-dimensional lattice models.
The main focus of the talk is on a systematic program that applies duality transformations, such as the decoration transformation, flipping relation, and star-square relation, to these newly discovered integrable models. These transformations generate a rich family of dual spin systems, including models with next-nearest-neighbor and multi-spin interactions.
The results illustrate the interplay between dual gauge theories and statistical mechanics, opening new avenues for exploring integrable systems and their dual counterparts.
References:
[1] D. N. Bozkurt, I. Gahramanov, and M. Mullahasanoglu, "Lens Partition Function, Pentagon Identity, and Star-triangle Relation", Phys. Rev. D 103 (2021) no.12, 126013
[2] I. Gahramanov, B. Keskin, D. Kosva, and M. Mullahasanoglu, "On Bailey Pairs for N = 2 Supersymmetric Gauge Theories on S3b/Zr", JHEP 03 (2023), 169
[3] M. Mullahasanoglu, "The Star–square Relation and the Generalized Star–triangle Relation from 3d Supersymmetric Dualities I", Eur. Phys. J. Plus 139 (2024) no.7, 643
[4] E. Catak and M. Mullahasanoglu, "Decorating the Gauge/YBE Correspondence", Eur. Phys. J. C 84 (2024) no.9, 962
[5] E. Catak and M. Mullahasanoglu, "Flipping Relation as a Reduced Star-star Relation", Eur. Phys. J. C 85 (2025) no.10, 1176
[6] M. Mullahasanoglu, "From Dual Gauge Theories to Dual Spin Models", Bulg. J. Phys. \textbf{52} (2025) no.s1, 114-119
Murat Özinan - Revealing the Underlying Physics of Gravitational Phase Transitions
Koç University, Department of Physics
Abstract: In some alternative theories of gravity, a phenomenon known as spontaneous scalarization leads to the formation of scalar clouds around compact objects. This phenomenon has attracted significant interest due to the large deviations it introduces from general relativistic spacetimes, which is particularly important in an era where we can probe the strong-field regime of gravity. Although scalarization has long been understood as a form of phase transition, it is only recently that phenomenological approaches have demonstrated that it is a first-order (discontinuous) phase transition across most of the theory’s parameter space. This is more than a theoretical curiosity, since the order of the transition affects what types of observables are possible from scalarized objects. In this talk we will demonstrate a new framework that enables us to predict the phase transition properties of scalarization starting from the nonlinear field equations. This circumvents the costly numerical computations, and also provides physical insight into many features of scalarization as a phase transition. We demonstrate why first-order phase transitions are dominant, and how the theory parameters influence perturbative orders, thereby reproducing previous results entirely from first principles and extending earlier investigations to different coupling choices. We will discuss the basic concepts of phase transitions, hence there is no need for prior knowledge of the topic.
Todor Popov - Time is a Jordan Superalgebra
Bulgarian Academy of Sciences, Institute for Nuclear Research and Nuclear Energy
Abstract: Time reparametrization in conformal quantum mechanics model of de Alfaro, Fubini and Furlan leads to a hidden dynamical Sp(2,R)-symmetry. The conformal time symmetry allows for a hierarchy of superconformal extensions Sp(2,R) ⊂ OSp(1|2) ⊂ OSp(2|2) ⊂ SU(1,1|2) known to describe the radial dynamics of a superparticle in vicinity of the event horizon of Reissner-Nordström black hole and also of a charged spin-1/2 particle in a magnetic monopole background.
We embed the (bosonic) time variable R into the tiny Kaplansky algebra JJ R^(1|2). We then see the above chain of superconformal embeddings through the lens of the Tits-Kantor-Koecher construction for Jordan superalgebra JJ R^(1|2). Our interpretation provides a unifying algebraic framework for superconformal quantum mechanics in external gauge/gravity fields.
Rasim Yılmaz - Double Field Theory as Double Copy of Yang-Mills Theory
Middle East Technical University, Department of Physics
Abstract: The Bern-Carrasco-Johansson (BCJ) double copy is a remarkable correspondence between gauge theories, such as Yang-Mills theory, and gravity. Originally discovered in the study of scattering amplitudes, this duality reveals deep structural similarities between these seemingly different physical theories. In addition to being at the center of the modern amplitude program, double copy idea is also extended to other frameworks, for example the construction of double field theory (DFT) action in perturbative manner. DFT is a framework that makes T-duality manifest by treating both the usual spacetime coordinates and their duals on an equal footing. In this talk, I give a brief summary to the construction of DFT action as a double copy of Yang-Mills theory, and extensions of this procedure to the Abelian sector of heterotic DFT and DFT on an arbitrary constant background.
References:
[1] Z. Bern, J. J. M. Carrasco, and H. Johansson, "New Relations for Gauge-theory Amplitudes", Phys. Rev. D 78, 085011 (2008), arXiv:0805.3993 [hep-ph].
[2] C. Hull and B. Zwiebach, "Double Field Theory", JHEP 09, 099, (2009), arXiv:0904.4664 [hep-th].
[3] F. Diaz-Jaramillo, O. Hohm, and J. Plefka, "Double Field Theory as the Double Copy of Yang-Mills Theory", Phys. Rev. D 105, 045012 (2022), arXiv:2109.01153 [hep-th].
[4] R. Yılmaz, "Towards the Double Copy Formulation for the Abelian Sector of Heterotic Double Field Theory", Eur. Phys.J. C 85, 1238 (2025), arXiv:2503.23425 [hep-th].
[5] R. Yılmaz, "Double Copy Map for Double Field Theory on an Arbitrary Constant Background", Phys. Rev. D 112, 066007 (2025), arXiv:2507.00500 [hep-th].