13th Tux Winter Workshop on Quantum Gravity

9 Feb 2026, 13:00 → 13 Feb 2026, 21:00 Europe/Berlin

Tux Center

The 13th Tux Winter Workshop on Quantum Gravity will take place on February 09–13, 2026 in the village of Tux in the Austrian Alps.

The idea for this series of workshops was conceived by Jerzy Lewandowski, who passed away in 2024. He shaped and nurtured these meetings for over a decade. His scientific rigour, humility and unique sense of humour are deeply missed.

Scope:

The workshops aim to bring together experts on loop quantum gravity and related topics. In general, the topics of the workshops include:

• All approaches to loop quantum gravity
• Other approaches to quantum gravity and their relation to LQG
• Quantum gravity phenomenology
• Quantum gravity topics of general interest
• General relativity and differential geometry topics of general interest

Invited speakers:

• Eugenio Bianchi (Pennsylvania State University)
• Roukaya Dekhil * (University of Florence)
• Kristina Giesel (FAU Erlangen-Nürnberg)
• Muxin Han * (Florida Atlantic University)
• Viktoria Kabel (ETH Zürich)
• Benjamin Knorr (Heidelberg University)
• Luca Marchetti (Okinawa Institute of Science and Technology)
• Tomasz Pawłowski * (University of Wrocław)
• Saeed Rastgoo (University of Alberta)
• Yuki Yokokura (KEK Theory Center)

* Online talk

Funding:

Funding for the workshop is provided by the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), the German Research Foundation (DFG), the National Centre for Nuclear Research (NCBJ, Poland) and the Universität Paderborn.

Earlier editions:

2025, 2024, 2023, 2022, 2020, 2019, 2018, 2017, 2016, 2015, 2014, 2013

Financial support and Visas:

We cannot provide any financial support for participants.

Please note that we can not support visa applications.

Organizers:

Mehdi Assanioussi, Christian Fleischhack, Ilkka Mäkinen, Hanno Sahlmann, Wolfgang Wieland

Monday 9 February

1 Bondi mass in black hole evaporation

In classical General Relativity, there is a clear distinction between Coulombic charges - such as the Bondi mass - and radiative fluxes. Their relation is encoded in flux-balance laws. In this talk, I discuss the semiclassical version of flux-balance laws, including quantum backreaction. In particular, I show how the quantum-corrected mass reduces to the Ashtekar-Taveras-Varadarajan proposal in 1+1 dimensions, and illustrate its implications for black hole evaporation in 3+1 dimensions.

Speaker: Eugenio Bianchi (Penn State)

2 The GUP black hole and its rotating counterpart: theory and phenomenology

Recently we derived the first metric of a nonsingular black hole in the framework of generalized uncertainty principle (GUP) (https://arxiv.org/abs/2406.03909, https://arxiv.org/abs/2412.08004). Despite its over 30 years of history, no black hole metric was systematically derived in GUP due to issues in applying GUP to field theories. We applied the tricks used in LQG to this system and it made it possible to derive such a metric. Furthermore, I discuss how we used the Newman-Janis formalism to derive the rotating counterpart of this black hole, and compared it to the data from the Event Horizon Telescope to set a bound on the quantum parameters of the model.

Speaker: Saeed Rastgoo (University of Alberta)

15:10 Break

3 Accessing the Spherically Symmetric Sector of LQG: A Framework for Quantum Gravitational Phenomenology

In this talk, I will present a mathematical framework that enables access to symmetric sectors within the full phase space of loop quantum gravity (LQG), offering a systematic approach to studying effective dynamics in a broad range of settings. Focusing on spherically symmetric solutions, this method of symmetry restriction is applicable to both cosmological and black hole spacetimes, and facilitates the construction of effective models that remain deeply rooted in the full theory. As an illustrative application, I will introduce new effective models for quantum cosmology and compare their features with existing LQG-inspired models in both spatially flat and closed universes. Our analysis reveals significant differences in the behaviour of these models as the curvature approaches the Planck regime, shedding light on key aspects of the pre- and post-bounce evolution. While the focus here is on cosmology, this framework also lays the foundation for future investigations into quantum gravitational effects in static and, more generally, rotating black holes.

Speaker: Jorden Roberts (University of Alberta)

4 Higher order black hole perturbations

Black hole perturbations in the Hamiltonian formalism are mostly considered up to second order. In this talk, we investigate the incorporation of perturbations beyond second order and the new technical challenges that arise.

Speaker: Jonas Neuser

5 From quantum Einstein-YM to observable signatures at large scales

I plan to cover the following topics: 1. Quantisation of Einstein-YM using a Hamiltonian-like formulation without space-time decomposition. 2. The appearance of the parameter $\varkappa$ related to the inverse "minimal volume" as an inherent part of quantisation (of differential forms). 3. The emergence of the canonical quantum YM in flat spacetime in the limiting case of infinite \varkappa. 4. A sketch of the proof relating the scale of \varkappa with the scale of the mass gap in quantum YM theory and the estimation of the cosmological constant. 5. A solution describing quantum Minkowski and quantum Einstein spacetimes. 6. A derivation of various modifications of Newtonian dynamics at large scales (including MOND). 7. Implications for dark matter and dark energy as macroscopic effects of quantum gravity. Based on: arXiv:2511.15025, arXiv:2311.05525, EPL 150, 59002 (2025), J. Phys.: Conf. Ser. 3017, 012031 (2025).

Speaker: Igor Kanatchikov (Natl. Quantum Information Center in Gdansk)

17:10 Break

6 Foundational Structure of Local Amplitudes in Quantum Gravity

There has been recently renewed interest in the quantisation of gravity by considering local subsystems on light-like hypersurfaces. In this talk, I will present a theory-independent framework that clarifies the common structure underlying these developments, assuming only standard quantum theory and general relativity.

The central idea is to describe local physics in terms of elementary light-like building blocks: three-dimensional null slabs bounded by past and future cuts. After briefly reviewing the timeless formulation of quantum theory, I will explain how to associate a kinematical Hilbert space to each null slab, with a natural factorization into bulk and corner degrees of freedom. Assuming the existence of appropriate vacuum states and a fundamental projector onto physical states, I will then show how local transition amplitudes can be constructed by gluing boundary data according to the causal structure of a diamond.

I will conclude by demonstrating that the resulting amplitudes satisfy Ward identities and charge conservation for the underlying symmetries, and by discussing how different approaches to quantum gravity may implement this framework in concrete settings.

Speaker: Charalampos Theofilis (FAU Erlangen-Nürnberg)

7 Fermionisation of the Aharonov–Bohm Phase on the Lightfront

We use a U(1) model to probe Loop Quantum Gravity on null surfaces. Starting from the electromagnetic phase space, we analyse the algebra between holonomies and fluxes. For a path (hoop) formed by two light-like segments connected by a space-like segment, we compute the Poisson brackets for the resulting holonomies. The result is a non-commutative Poisson algebra of holonomies. Two hoop-holonomies commute unless they cross the same light-ray. Upon quantization, holonomies on the light-cone behave effectively as fermions, offering a tractable framework for LQG-type quantization on null geometry.

Speaker: Carolina Sole Panella (FAU Erlangen-Nürnberg)

18:40 Discussion

Tuesday 10 February

8 An ultraviolet fix point of Lorentzian spinfoam quantum gravity

We investigate the ultraviolet behavior of Lorentzian spinfoam quantum gravity by summing over 2-complexes, addressing the problem of infinite ambiguities relating to the triangulation dependence. We introduce spin-network stacks and their covariant extension, spinfoam stacks, which sum over families of 2-complexes generated by stacking faces onto root complexes. We demonstrate that the state sum exhibits an analog Bose-Einstein condensation phenomenon, where quantum geometry condenses to a dominant small spin configuration. In the large spin cut-off limit, the amplitudes localize to a topological theory. In this limit, the infinitely many ambiguities relating to triangulation dependence reduce to only finitely many degrees of freedom that are only associated to the boundary.

Speaker: Muxin Han

9 From Principles to Effective Models: A Constructive Framework for Effective Covariant Actions with a Unique Vacuum Solution

Birkhoff's theorem guarantees a unique vacuum sector in classical general relativity. Many effective quantum gravity models lack this property, leading to a fundamental ambiguity in the choice of vacuum solution and complicating phenomenological analyses that may depend on such a choice. This talk discusses a constructive framework that addresses this problem by deriving fully 4D-covariant actions using, on the one hand, the physical properties of the degrees of freedom involved, namely dust and gravity, and, on the other hand, two further guiding principles: spatial diffeomorphism invariance and a geometric guiding principle. In these models, the dynamics decomposes into independent LTB shells. The imposition of spatial diffeormorphism invariance together with a geometric principle, that guarantees a unique static vacuum solution, severely restricts the form of the shell Hamiltonian and the vacuum metric. The class of covariant actions reconstructed in this framework belongs to the class of generalised extended mimetic gravity models. Finally, the extent to which this framework provides a consistent basis for perturbation theory beyond the static sector and offers new insights into the ambiguity of curvature polymerisation in loop quantum cosmology is discussed.

Speaker: Kristina Giesel (FAU Erlangen-Nürnberg)

15:10 Break

10 Hamiltonian renormalisation of the U(1)^3 model for 3+1 quantum gravity

We apply Hamiltonian renormalisation to Smolin's U(1)^3 model for 3+1 quantum gravity which can be considered as a weak Newton constant regime of the full theory.
We find that the renormalisation group flow indeed finds known solutions of this
model as fixed point. This suggests that the renormalisation scheme can be used
also for the full theory with the aim to fix quantisation ambiguities.

Speaker: Melissa Rodriguez Zarate (Friedrich Alexander University)

11 QED in Ashtekar-Barbero variables and its implications

We explore the modifications to fundamental geometric variables of Loop Gravity induced by the presence of fermions, and examine the resulting gravitational dynamics. This analysis is then extended to incorporate Quantum Electrodynamics (QED). Finally, we discuss potential approaches for quantizing the system, outlining possible directions for future research.

Speaker: Federica Fragomeno (University of Alberta)

12 The impact of a quantum space-time determined by the canonical quantization of unimodular gravity on modelling our Universe

Cosmological models of our universe are based on relations between the scale factor, the Hubble parameter and the matter density determined by general relativity combined with simplified matter models. We investigate the quantum analogue of these relations by implementing the results for expectation values of the operators representing the quantum counterparts of the cosmological parameters for perfect fluid quantum cosmological models derived from the canonical quantization of unimodular gravity which is equivalent to general relativity on the classical level. We further discuss the role of quantum uncertainties evolving in time for quantum deviations in general and causality in particular.

Speaker: Natascha Riahi (University of Vienna)

17:10 Break

13 Physical projection from spinfoam amplitudes

In this talk, we analyze the functional properties of spinfoams independently of any specific model. We propose a set of axioms for defining a spinfoam model, inspired by Atiyah’s axioms for Topological Quantum Field Theory (TQFT) at the discrete level. Building on this framework, we introduce a precise notion of the refinement limit, from which we derive the properties of the spinfoam transition amplitude in the continuum. Assuming a natural convergence condition for this limit, we prove that the theory defines a rigging map. Consequently, the construction yields a unique candidate for the physical Hilbert space of the theory, allowing us to characterize physical states directly from truncated spinfoam amplitudes.

Speaker: Matteo Bruno (Sapienza University of Rome)

14 Normalisability, Correlation, and Operator Ordering in Physical Solutions of the Thiemann Hamiltonian in Abelian LQG

In this talk, we present recent progress on applying efficient, deep-learning-inspired numerical techniques to solving quantum constraints in canonical loop quantum gravity (LQG) models. Focusing on the 4-dimensional weak coupling model of LQG, we approximate and analyse physical solutions of the Thiemann regularised quantum Hamilton constraint and characterise their structure and physical properties. To name a few, we show that such solutions exhibit long-range correlation, we investigate their normalisability and the geometries which they represent. We also demonstrate how different constraint orderings can be systematically compared.

We illustrate the broader applicability of this approach to a range of LQG settings, including quantum reduced loop gravity and selected spherically symmetric models. Finally, we show that in principle, the developed methods enable large-scale simulations of graph-non-enlarging LQG models with arbitrarily large cutoffs on the degrees of freedom and arbitrarily complex underlying graphs, all at tractable computational cost. We conclude with an outlook and roadmap for extending this programme to full SU(2) models and potentially to genuinely graph-changing dynamics.

Speaker: Waleed Sherif (Friedrich-Alexander-Universität Erlangen Nürnberg (FAU))

18:40 Discussion

Wednesday 11 February

15 Asymptotically safe scattering amplitudes and the infrared jungle

I discuss a simple model in which a scattering amplitude can be computed analytically, based on an asymptotically safe fixed point. I will present the analytical structure of the amplitude, and a potential realisation of the no global symmetries conjecture previously thought to be incompatible with asymptotic safety. A key feature of the amplitude is the appearance of gravitational logarithms, which are large in purely massless theories, but can potentially be tamed in massive theories as long as there is a scale separation of the mass and the Planck scale.

Speaker: Benjamin Knorr (Heidelberg University)

16 Probing linearised quantum gravity with a test particle

In classical general relativity, we measure the gravitational field indirectly by probing it with test particles and fields. In this talk, I want to address to what extent we can do the same in the quantum theory, focusing on the low-energy regime of quantum gravity, which has seen much recent progress through the use of tools from quantum information theory. There are two challenges when trying to model a test particle probing the quantum state of the gravitational field: one technical, the other more fundamental. On the technical side, one needs to find the appropriate approximation to obtain a tractable problem. After discussing briefly some of the possible strategies, we will focus on a Born-Oppenheimer approximation, treating the linearised quantum gravitational field as a slow background degree of freedom, compared to a light test particle. More fundamentally, probing the quantum state of the gravitational field indirectly, i.e. without direct access to the gravitational field itself, means that we have to trace out the gravitational degrees of freedom, generally leading to a loss of coherence also in the test particles’ state. The question thus arises to what extent we can make inferences about the quantum properties of the gravitational field by measurements on the test particle alone.

Speaker: Viktoria Kabel

15:10 Break

17 Toward Quantum Gravity from Pure Shape Dynamics

The plethora of conceptual and technical problems of Quantum Gravity (QG) does not indicate the futility of this quest per se or non-existence thereof. Rather, we face multiple incomplete approaches that have been developed, all reflecting some expected aspects of QG. The absence of a unique theory is especially evident in the renormalization approach to gravity, where coarse-grained effective physics cannot determine a single theory due to the infinite-dimensional critical surface. These difficulties call for a more constrained framework built on strong, selective principles. We propose Pure Shape Dynamics (PSD) as one such approach. Motivated by the idea that local physical data refer only to relations within material structures, PSD posits scale-invariant, purely relational configurations (shapes) as the sole physical degrees of freedom from which gravity and geometry emerge. This imposes non-trivial constraints on the formalism. The PSD formulation of dynamical geometry^1 shows how absolute scale and time can be removed to yield a fully relational description. Starting from the ADM formulation of GR, we derive a decoupled dynamical system governing the evolution of spatial conformal geometry and relational matter degrees of freedom, while eliminating the scale factor as an independent variable. Crucially, this autonomous system fully recovers the empirical content of GR and, remarkably, is derived purely algebraically without solving the non-linear Lichnerowicz-York and lapse-fixing differential equations. This demonstrates gravity as emergent from the dynamics of 3D spatial conformal geometry and, more importantly, suggests a suitable kinematics for a QG. The strategy is as follows. We posit a finite number of points, each equipped with Weyl spinors, within a conformal geometry. Relational reference structures arise from conformal geodesics – namely, generalized circles – requiring tangent and acceleration vectors, encoded in the spinor pairs at each vertex. The transport of this system with a conformally covariant connection reveals the conformal curvature, which can be explored analogously to the spatial curvature using the Ashtekar connection in LQG. Hence, a construction parallel to the kinematic Hilbert space of LQG is expected to ground the dynamical Hilbert space of Quantum PSD. Such a model with finite, yet arbitrarily large, degrees of freedom describes a regularized quantum gravity. To address the classical limit, under a suitable coarse-graining procedure, this model is expected to describe an effective dynamical system of conformal geometry – the very framework developed in PSD for classical gravity.

(1) P. Farokhi, T. Koslowski, P. Naranjo (2025): “Pure Shape Dynamics: Relational Dynamical Geometry”. arxiv:2503.00996

Speaker: Pooya Farokhi (University of Cologne)

18 q-Desics, Motion in Quantum-Gravitational Backgrounds

We address the motion of test particles in quantum-gravitational backgrounds by introducing the concept of q–desics, quantum-corrected analogs of classical geodesics. Unlike standard approaches that rely solely on the expectation value of the spacetime metric, our formulation is based on the expectation value of quantum operators, such as the affine connection operator. This allows to capture richer geometric information. We derive the q–desic equation using both Lagrangian and Hamiltonian methods and apply it to spherically symmetric static backgrounds obtained from canonical quantum gravity. Exemplary results include lightlike radial motion and circular motion with quantum gravitational corrections far above the Planck scale. This framework provides a refined description of motion in quantum spacetimes and opens new directions for probing the interface between quantum gravity and classical general relativity.
Note: ArXiv paper pitch: https://youtu.be/sf3A2qnE3F4

Speaker: Benjamin Koch (TU-Wien ITP und Atominstitut)

19 Doubly special relativistic spacetime picture and the phenomenology of Planck-scale-modified time dilation

The most active area of research in quantum-gravity phenomenology investigates the possibility of Planck-scale-modified dispersion relations, focusing mainly on two alternative scenarios: the Lorentz invariance violation (LIV) scenario, characterized by a specific mechanism of breakdown of relativistic symmetries, and the “DSR” scenario, which preserves overall relativistic invariance but with deformed laws of relativistic transformation. Two recent studies of modified dispersion relations, one relying on Finsler geometry and one based on heuristic reasoning, raised the possibility of potentially observable effects for time dilation and argued that this might apply also to the LIV and DSR scenarios. We observe that the description of Lorentz transformations in the LIV scenario is such that time dilation cannot be modified. The DSR scenario allows for modifications of time dilation, and establishing their magnitude required us to obtain novel results on the effects of finite DSR boosts in the spacetime sector, with results showing in particular that the modification of time dilation is too small for experimental testing.

Speaker: Marco Refuto (University of Naples ''Federico II'')

17:10 Break + Discussion

Public Talk: Black Holes' Seven Wonders

Convener: Eugenio Bianchi (Penn State)

Thursday 12 February

20 Cosmic Acceleration from Quantum Gravity: Emergent Inflation and Dynamical Dark Energy

Recent cosmological observations increasingly challenge the standard picture of cosmic acceleration, pointing toward an evolving dark-energy sector—possibly with phantom characteristics—and by placing considerable pressure on even the better-theoretically motivated inflationary models. In this talk, I present a new mechanism for cosmic acceleration arising from quantum gravity interactions in (mean-field) Group Field Theories (GFTs). Depending on the interaction type, the resulting cosmological dynamics can either feature a late-time attractor corresponding to a dynamical dark energy phase—often with characteristic phantom behavior, including in models inspired by simplicial gravity—or instead support an early slow-roll inflationary epoch driven by the same underlying quantum-gravitational effects. This emergent inflation, effectively captured by a single-field description, can sustain the required expansion, naturally avoids the graceful exit problem, and appears to transition into a persistent, non-accelerating phase consistent with classical expectations. I conclude by outlining prospects for further developments.

Speaker: Luca Marchetti (Okinawa Institute of Science and Technology)

21 Quantum Black Hole from Quantum Mattar

Quantum effects of matter are indispensable for revealing the true nature of black holes; the time evolution of quantum states during collapse and evaporation, the origin of the entropy-area law, and the back-reaction of quantum fluctuations of matter fields on spacetime with high curvatures. In various approaches, we obtain a non-perturbative self-consistent solution to the semi-classical Einstein equation. It represents a compact dense configuration without a horizon. A quantum pressure consistent with 4D Weyl anomaly arises inside, eliminating classical singularities. Integrating the entropy density of the matter fields over volume exactly reproduces the entropy-area law due to self-gravity. The imaging is consistent with that of the classical black hole. Furthermore, an effective dynamics beyond the semi-classical approximation describes the interior fully up to r=0. This talk will outline these results.

Speaker: Yuki Yokokura

15:10 Break

22 Loop quantum cosmology quantization of homogeneous dust collapse

In classical general relativity, the gravitational collapse of matter inevitably leads to the formation of a spacetime singularity. Numerous works have shown that introducing loop quantum gravity corrections at the semiclassical level resolves the singularity by replacing it with a bounce. Nevertheless, a fully quantum treatment of the problem has remained largely unexplored.
In this talk, I will present the loop quantum cosmology quantization of a spherically symmetric, homogeneous cloud of pressureless dust, providing a fully quantum treatment of its dynamics.
The key feature that allows the direct quantization is the classical deparametrization of the system into independently evolving shells, each of which can be quantized separately. Through a numerical analysis, I will show that every shell undergoes a unitary evolution avoiding the singularity by means of a bounce. Finally, I will discuss the expectation values of the volume and density operators in order to draw a comparison with the semiclassical limit aforementioned.

Speaker: Luca Cafaro (University of Warsaw)

23 Gravitational collapse in effective loop quantum gravity and the formation of shell-crossing singularities

In this talk the investigation of the gravitational dust collapse within the framework of effective loop quantum gravity will be addressed with a special focus on the properties and the formation of shell-crossing singularities in these models. The specific effective gravitational collapse model that will be discussed in this talk is based on the cosmological Hamiltonian derived from full LQG by Dapor and Liegener using coherent state techniques in the AQG framework for LQG. This model is characterized by an unsymmetric bounce as its central feature. The investigation of the resulting effective dynamics will be presented in detail and differences and similarities compared to other existing models will be discussed. In a broader context, the question of the existence of shell-crossing singularities is investigated beyond the specific model, including also models subject to unbounded polymerisation functions, such as the regular black hole models of Bardeen and Hayward.

Speaker: Eric Rullit

24 Exploring Gravitationally Induced Decoherence Models: Properties and Implications

Gravitationally induced decoherence is discussed in the framework of open quantum systems by coupling matter systems to linearised gravity as an environment. The construction and investigation of corresponding quantum mechanical toy models are examined to illustrate how the gravitational coupling may lead to decoherence effects. These models are compared with existing approaches in the literature for their similarities and differences, with a focus on the assumptions involved and their implications. The role of different quantisation techniques and their impact on the structure of the resulting models is also briefly addressed.

Speaker: Roman Kemper (Friedrich Alexander Universität Erlangen-Nürnberg)

17:10 Break + Discussion

19:00 Workshop Dinner

Friday 13 February

25 Emergent scalar field dynamics on curved spacetime in Group Field Theory

Working within the relational framework of group field theories and specifically its application to
cosmology, we derive an explicit solution to the GFT condensate effective dynamics, including the
treatment of scalar perturbations. This first step allowed us to investigate further the matter content
and formulate its dynamics in the form of QFT on a curved background. This, in turn, produced
additional emergent properties that the field theory possesses in comparison with the classical one,
which was further mirrored at the level of the perturbation. In the latter case, we attained a modified
dispersion relation for the perturbed field.

Speaker: Roukaya Dekhil

26 TBA

Speaker: Tomasz Pawłowski

15:10 Break

27 Time evolution of semiclassical states in the one-vertex model of quantum-reduced loop gravity

We consider the dynamics in quantum-reduced loop gravity generated by a specific choice of the physical Hamiltonian operator, where the Lorentzian part of the Hamiltonian is given by an operator representing the scalar curvature of the spatial manifold. Specializing to a cubic graph consisting of a single six-valent vertex, and truncating the Hilbert space of the model by introducing a finite but relatively large cutoff on the spin quantum numbers, the time evolution of quantum states becomes accessible through numerical computations. We present results for the quantum dynamics of semiclassical states describing homogeneous and isotropic spatial geometries, and compare the evolution of geometrical observables against the "effective dynamics" generated on the classical phase space by a semiclassical effective Hamiltonian.

Speaker: Ilkka Mäkinen (National Centre for Nuclear Research, Poland)

28 Coarse-graining and elementary blocks of LQG

Speaker: Mehdi Assanioussi

16:40 Discussion