Athanasios Chatzistavrakidis was awarded with NAWA's Ulam Fellowship and will join us for six month

Since May 2022, we implement the research programme

Duality Symmetries as Key to Quantum Spacetime

funded by the SONATA BIS grant 2021/42/E/ST2/00304 awarded by the National Science Centre (the largest grant-making agency in Poland for fundamental research and basic science). With these funds from the NCN, we establish a new research, independent research team at the University of Wrocław. We are always looking for new team members! For details please check the vacancies below.

We are also members of the COST actions

CA21109 - Cartan geometry, Lie, Integrable Systems, quantum group Theories for Applications (CaLISTA)
CA22113 - Fundamental challenges in theoretical physics (THEORY-CHALLENGES)

Mission

The Einstein Hilbert action is not renormalisable in more than two dimensions. Thus, it can only represent the leading contribution to an effective action that receives higher-order (curvature/derivative) corrections. These corrections are vital when gravity dominates the other three fundamental forces, i.e. close to the singularity of a black hole or at the beginning of our universe. They eradicate the standard geometric notion of space and time, which must be replaced by the more elaborate concept of quantum spacetime. One of the big puzzles of modern theoretical physics therefore is:

What are the fundamental properties of quantum spacetime?
What is the appropriate mathematical framework to describe it?

We address both systematically.

Interactions with matter and energy dynamically shape spacetime, but currently, progress is only possible for a particular subclass of spacetimes governed by powerful symmetries. They provide the computational control inevitable to approach the questions above but can be very restrictive at the same time and kill all non-trivial phenomena. We manage the balancing act by introducing the quantum version of Poisson-Lie symmetry inspired by the closed string $\sigma$ -model and its tight connection to gravity. Thereby, we obtain consistent quantum spacetimes, which are crucial in understanding central quantum gravity phenomena, like the resolution of singularities, holography, and flux vacua in string theory.

We study quantum corrections for the large class of Poisson-Lie symmetric closed string $\sigma$ -models. The relevant computations are infamous for their complexity, and despite significant effort, only results for the first subleading order are known. We make progress by employing the working hypothesis: "Poisson-Lie symmetry and T-duality can be defined beyond the classical limit." for which considerable evidence piled up during the last two years. All relevant spacetimes will be embedded in an appropriately extended version of double field theory to make their hidden Poisson-Lie symmetry manifest. Once manifest, this symmetry is so powerful that it facilitates explicit loop calculations up to high orders in perturbation theory. It can appear in combination with the integrability of the σ-model or supersymmetry. We will determine how these symmetries constrain higher derivative corrections of the effective action and ultimately induce the transition from spacetime to quantum spacetime. To achieve these objectives, we pursue three main research tasks:

Develop quantum, $\alpha$ '-corrected, Poisson-Lie symmetry and T-duality
Understand implications of 1. for integrable $\sigma$ -models and holography
Formulate resulting target space structures in terms of non-commutative geometry

Publications

Implementing these research tasks resulted until now in the following publications authored by at least on of our group's members.

[H1]

F. Hassler, Y. Sakatani, L. Scala: Generalized Dualities for Heterotic and Type I Strings, preprint December 2023, arXiv:2312.16283, abstract

We define generalized dualities for heterotic and type I strings based on consistent truncations to half-maximal gauged supergravities in more than three dimensions. The latter are constructed from a generalized Scherk-Schwarz ansatz in heterotic double field theory that satisfies the strong constraint. Necessary and sufficient conditions on the resulting embedding tensor are discussed, showing that only certain gaugings, called geometric, can arise from this procedure. For all of them, we explicitly construct the internal geometry and gauge potentials. In general, this construction is not unique and permits different uplifts which are used to define generalized T-duality. Two examples are worked out underlying the utility of our approach to explore new dualities and uplifts of half-maximal gauged supergravities.

[L1]

E. Lescano, N. Mirón-Granese, Y. Sakatani: O

(D,D)

-covariant formulation of perfect and imperfect fluids in the double geometry, Phys. Rev. D 109 (2024), arXiv:2312.03610, abstract

We study generic matter coupled to a $D$ -dimensional supergravity using a formulation of Double Field Theory (DFT), where all the fields are encoded in O $(D,D)$ multiplets. We study both the case when the matter comes from a variational principle, as well as the case where the matter comes from a statistical or thermodynamic approach. For the latter, we construct the distribution function for the perfect fluid and its entropy current, which is a conserved quantity. We then include general viscous and elastic terms in the generalized energy-momentum tensor which, in the general case, lead to entropy production. We consistently deform the conservation law of the generalized entropy current and identify a particular non-dissipative deformation. Using the generalized fluid model, we revisit the issue of non-covariance of perfect fluids under T-dualities and we show how to resolve it in our DFT model with matter.

[H2]

F. Hassler, Y. Sakatani: The Hierarchy of Curvatures in Exceptional Geometry, preprint November 2023, arXiv:2311.12095, abstract, Citations: 1

Despite remarkable success in describing supergravity reductions and backgrounds, generalized geometry and the closely related exceptional field theory are still lacking a fundamental object of differential geometry, the Riemann tensor. We explain that to construct such a tensor, an as of yet overlooked hierarchy of connections is required. They complement the spin connection with higher representations known from the tensor hierarchy of gauged supergravities. In addition to solving an important conceptual problem, this idea allows to define and explicitly construct generalized homogeneous spaces. They are the underlying structures of generalized U-duality, admit consistent truncations and provide a huge class of new backgrounds for flux compactifications with non-trivial generalized structure groups.

[H3]

F. Hassler, S. Lacroix, B. Vicedo: The Magic Renormalisability of Affine Gaudin Models, JHEP 12 (2023), arXiv:2310.16079, abstract, Citations: 4

We study the renormalisation of a large class of integrable $\sigma$ -models obtained in the framework of affine Gaudin models. They are characterised by a simple Lie algebra $\mathfrak{g}$ and a rational twist function $\varphi(z)$ with simple zeros, a double pole at infinity but otherwise no further restrictions on the pole structure. The crucial tool used in our analysis is the interpretation of these integrable theories as $\mathcal{E}$ -models, which are $\sigma$ -models studied in the context of Poisson-Lie T-duality and which are known to be at least one- and two-loop renormalisable. The moduli space of $\mathcal{E}$ -models still contains many non-integrable theories. We identify the submanifold formed by affine Gaudin models and relate its tangent space to curious matrices and semi-magic squares. In particular, these results provide a criteria for the stability of these integrable models under the RG-flow. At one loop, we show that this criteria is satisfied and derive a very simple expression for the RG-flow of the twist function, proving a conjecture made earlier in the literature.

[H4]

Daniel Butter, Falk Hassler, Christopher N. Pope, Haoyu Zhang: Generalized Dualities and Supergroups, JHEP 12 (2023), arXiv:2307.05665, abstract, Citations: 1

Using a recently developed formulation of double field theory in superspace, the graviton, $B$ -field, gravitini, dilatini, and Ramond-Ramond bispinor are encoded in a single generalized supervielbein. Duality transformations are encoded as orthosymplectic transformations, extending the bosonic O( $D$ , $D$ ) duality group, and these act on all constituents of the supervielbein in an easily computable way. We first review conventional non-abelian T-duality in the Green-Schwarz superstring and describe the dual geometries in the language of double superspace. Since dualities are related to super-Killing vectors, this includes as special cases both abelian and non-abelian fermionic T-duality. We then extend this approach to include Poisson-Lie T-duality and its generalizations, including the generalized coset construction recently discussed in arXiv:1912.11036. As an application, we construct the supergeometries associated with the integrable $\lambda$ and $\eta$ deformations of the AdS $_5 \times$ S $^5$ superstring. The deformation parameters $\lambda$ and $\eta$ are identified with the possible one-parameter embeddings of the supergravity frame within the doubled supergeometry. In this framework, the Ramond-Ramond bispinors are directly computable purely from the algebraic data of the supergroup.

[S1]

G. Fabiano, G. Gubitosi, F. Lizzi, L. Scala, P. Vitale : Bicrossproduct vs. twist quantum symmetries in noncommutative geometries: the case of

\rho

-Minkowski, JHEP 08 (2023), arXiv:2305.00526, abstract

We discuss the quantum Poincaré symmetries of the $\rho$ -Minkowski spacetime, a space characterised by an angular form of noncommutativity. We show that it is possible to give them both a bicrossproduct and a Drinfel’d twist structure. We also obtain a new noncommutative $\star$ -product, which is cyclic with respect to the standard integral measure.

[H5]

F. Hassler, Y. Sakatani: All maximal gauged supergravities with uplift, Prog. Theor. Exp. Phys. 2023 (2023), arXiv:2212.14886, abstract, Citations: 7

Recent progress in generalised geometry and extended field theories suggests a deep connection between consistent truncations and dualities, which is not immediately obvious. A prime example is generalised Scherk-Schwarz reductions in double field theory, which have been shown to be in one-to-one correspondence with Poisson-Lie T-duality. Here we demonstrate that this relation is only the tip of the iceberg. Currently, the most general known classes of T-dualities (excluding mirror symmetry) are based on dressing cosets. But as we discuss, they can be further extended to the even larger class of generalised cosets. We prove that the latter give rise to consistent truncations for which the ansatz can be constructed systematically. Hence, we pave the way for many new examples of T-dualities and consistent truncations. The arising structures result in covariant tensors with more than two derivatives and we argue how they might be key to understand generalised T-dualities and consistent truncations beyond the leading two derivative level.

[H6]

D. Butter, F. Hassler, C. Pope, H. Zhang: Consistent Truncations and Dualities, JHEP 4 (2023), arXiv:2211.13241, abstract, Citations: 5

News

To keep you updated, here are the lastest updates.

03.11.23: David Osten awarded with internship at the German Bundestag from Heraeus Foundation
Congratulation to David, who was select from the Wilhelm and Else Heraeus Foundation for an internship at the German Bundestag. This internship is the secondment of his Polonez BIS grant and will give David the opportunity to experience the work of the German government first hand.
01.12.23: Athanasios Chatzistavrakidis was awarded with NAWA's Ulam Fellowship and will join us for six month
We are very happy that Thanasis (Athanasios Chatzistavrakidis), who is an senior research associate (associate professor) at the Ruđer Bošković Institute in Zagreb, Croatia, will join our goup at the end of this year for six month. He was awarded with a Ulam Fellowship for NAWA.

Visitors

Thanks to the support of the NCN, we are able to regularly invite visitors. If you are interested in visiting our group, please contact me or David. For everyone who is visiting us: We compiled for your convenience a couple of information about visiting Poland and Wrocław in particular. Already established visits in reverse chronological order are:

Martin Cederwall, Chalmers University of Technology, 6th - 12th October 2024, invited by Falk Hassler
Sylvain Lacroix , ETH Zürich, 23rd - 28th June 2024, invited by David Osten
Axel Kleinschmidt, Max Planck Institute for Gravitational Physics (Albert Einstein Institute), 16th - 22nd June 2024, invited by David Osten
Marcus Sperling, University of Vienna, 17th - 20th April 2024, invited by Falk Hassler, details
Marcus will give a talk in our institute seminar on Friday, 19. April 2024, 12:15 in room 422. Everyone is welcome to join.

"Symplectic Singularities in Physics: Their Origins and Significance"

Abstract: Symplectic singularities, also known as hyper-Kahler singularities, encompass well-known geometric spaces such as the Kleinian surface singularities or the moduli space of instantons. Recently, a new class of symplectic singularities has emerged through the construction based on a physics model known as the 3d $N=4$ Coulomb branch. In this presentation, I aim to provide an introduction and overview of symplectic singularities in general, with a particular focus on the 3d $N=4$ Coulomb branches. I will place special emphasis on the symplectic singularities that manifest as moduli spaces of vacua within supersymmetric field theories containing 8 supercharges in space-time dimensions ranging from 3 to 6. These instances showcase how geometric features offer elegant descriptions of strongly coupled phenomena.
Riccardo Borsato, University of Santiago de Compostela, 3rd - 9th December 2023, invited by Falk Hassler, details
Riccardo will give a talk in our division seminar on Tuesday, 5. December 2023, 14:15 in room 422. Everyone is welcome to join.

"Deformations of 2D field theories and the light-cone gauge"

Abstract: Recently, there has been a lot of progress in the construction of deformations of 2-dimensional integrable field theories that do not break the original integrability. Often, the motivation is related to the realisation of such integrable models in the context of the holographic duality, thus opening the possibility to obtain exact results for gauge and gravity theories and their deformations. At the same time, the study of such deformations has led to some puzzles that force us to better understand already the undeformed models. In particular, in this talk I will explain why it is important to carefully choose the light-cone gauge (necessary to fix the reparameterisation invariance on the worldsheet of the string) in order to have a workable description of the deformed models, and I will show how inequivalent light-cone gauges are related to each other.
Linus Wulff, Masaryk University, 5th - 11th November 2023, invited by Falk Hassler, details
Linus will give a talk in our division seminar on Tuesday, 7. November 2023, 14:15 in room 422. Everyone is welcome to join.

"Stringy corrections to gravity from dualities"

Abstract: As a quantum theory of gravity, string theory predicts specific corrections to Einstein's theory. These corrections are in general difficult to compute. I will describe an approach that uses another characteristic feature of string theory - the existence of dualities - to constrain the form these corrections can take.
Sibylle Driezen, ETH Zürich, 23rd - 27th October 2023, invited by David Osten, details
Sibylle will give a talk in our division seminar on Tuesday, 24. October 2023, 14:00 in room 422. Everyone is welcome to join.

"Exploring integrable deformations"

Abstract: Recent years have seen an upsurge of interest in deformations of two-dimensional sigma-models which preserve classical integrability when present in the original model. This property enables powerful techniques for solving these models, even in non-trivial scenarios such as at strong coupling. This talk introduces classical integrability concepts and reviews the construction of a large family of integrable deformed sigma-models. We will focus on the crucial role played by "worldsheet dualities", which have been naturally developed within the context of string theory. In the second part of the talk, we will explore the interest of applying integrable deformations on the so-called AdS/CFT correspondence, a duality connecting highly symmetrical string theories to gauge theories. Specifically, we will focus on the “Jordanian” subclass of integrable deformations and provide insights into ongoing research in this area.
Chris Blair, Autonomous University of Madrid, 2nd - 8th July 2023, invited by Falk Hassler, details
Chris will give a talk on Tuesday, 4. July 2023, 14:00 in room 119. Everyone is welcome to join.

"Generalised U-duality"

Abstract: Supergravity inherits T- and U-duality symmetry from string and M-theory. These dualities can be used to map solutions with abelian isometries to other solutions with abelian isometries. There also exist "generalisations" of these dualities involving transformations between solutions with more complicated symmetries, or even without isometries. The most studied examples are generalised T-dualities (such as non-abelian and Poisson-Lie T-duality) which have been known for many years. Only recently, thanks in large part to the use of generalised geometry, has it been understood how to obtain similar generalisations of the U-duality symmetry of 11-dimensional supergravity. I will explain a particular realisation of this idea, loosely covering my papers 2006.12452, 2203.01838, 2205.13019 and 2210.07867.
Fiona Seibold, Imperial College London, 14th - 20th May 2023, invited by David Osten, details
Fiona will give a talk on Wednesday, 17. May 2023, 11:00 c.t. in room 119. Everyone is welcome to join.

"Integrable deformations of AdS3 superstrings"

Abstract: Solving string theory on curved backgrounds is a challenging endeavour. Sometimes we are in the lucky position where the string theory is integrable, meaning that there are many hidden conserved charges, and the theory is in principle exactly solvable. This is the case for instance of strings propagating in an AdS $_3$ xS $^3$ xT $^4$ background. In this talk I will present recently constructed multi-parameter deformations of AdS $_3$ superstrings that preserve the integrable structure. Generically, these deformations break all the supersymmetries and have a hidden quantum group symmetry. In the special case of AdS $_3$ , half of the original supersymmetries can be preserved, and the deformed backgrounds share some "nice" properties with the undeformed one, which makes their analysis particularly interesting in the context of the AdS/CFT correspondence. I will also discuss how the different integrable deformations are related through extended (Poisson-Lie) worldsheet dualities.
David Osten, Ludwig Maximilians University Munich, 22nd - 25th January 2023, invited by Falk Hassler, details
This is David's inauguration visit to Wrocław. He will tell us more about his research on Monday, the 23rd of January at 14:30 (room 416), in his talk

"New classically integrable $\sigma$ -models based on $\mathbb{Z}(N)$ -symmetric homogeneous spaces"

Abstract: Typical two dimensional integrable $\sigma$ -models are those which have group manifolds or Riemannian symmetric spaces, or in other words homogeneous spaces with a $\mathbb{Z}(2)$ -grading, as target spaces. This construction can be generalised to homogeneous spaces based on a $\mathbb{Z}(N)$ -grading. After a review of these $\sigma$ -models and their classical integrability, I present new types of $\sigma$ -models with $\mathbb{Z}(N)$ -symmetric homogeneous target spaces and some of their deformations. I comment on the geometric interpretation of the $\mathbb{Z}(N)$ -symmetry, the applicability as string $\sigma$ -models and Hamiltonian integrability.
Eric Lescano, Ruđer Bošković Institute, 13th - 15th November 2022, invited by Falk Hassler, details
Eric will give a talk on Monday, the 14th on November 14:30, at our division's weekly seminars with the title

"Statistical matter coupled to the (double) geometry"

Abstract: This talk will be about cosmology and string theory and it will have two parts. In the first one we will review the inclusion of statistical matter in Riemannian geometries. Our starting point will be the Einstein equation and we will focus on energy-momentum tensors that depend on hydrodynamics/thermodynamics variables, such as the perfect fluid. We will derive conservation laws considering relativistic kinetic theory. We will finish this part with a quick introduction to the low energy limit of string theory (supergravity) and its Double Field Theory (DFT) rewriting.

Members

As a group, we are united by the desire to better understand the fundamental structure of spacetime and how it is shaped by gravity. We treat physics as a team sport and therefore enjoy discussions, and sharing our knowledge with each other on a daily basis. Our team members are:

Current Members

Falk Hassler
Group leader
E-Mail:
Website:

www.fhassler.de
Office:
448
Falk is the head of the group. More information on him can be found at the landing page and in his CV.
David Osten
Principal Investigator
Period:
01.03.23 - now
E-Mail:
Website:

sites.google.com/view/david-osten
Office:
442
David is the PI of the Polonez BIS grant 2022/45/P/ST2/03995 and joined our group in March of 2023. He is an expert in exceptional generalised geometry, non-linear $\sigma$ -models in more than two dimensions and classical integrability. In 2020, he obtained his PhD in theoretical physics at the Max Planck Institute for Physics in Munich, followed by postdoc positions at ITMP of the Lomonosov Moscow State University and Ludwig Maximilian University Munich. We work with him towards a better understanding of membrane theories and their relation to exceptional field theory.
Eric Lescano
Postdoc
Period:
03.10.23 - now
E-Mail:
Office:
448A
Eric is an expert in dualities, their implications for higher-derivative corrections, and their applications spanning from cosmology to the double copy formalism. After completing his PhD degree at the Universidad de Buenos Aires in 2021, he came to Europe for his first postdoc at the Institut Rudjer Boskovic in Croatia. Now he is here in Wroclaw for his second postdoc, where we are exploring the interplay between higher-derivative corrections in string theory and generalized dualities.
Achilles Gitsis
PhD student
Period:
01.10.22 - now
E-Mail:
Office:
444
Achilles Gitsis became a PhD student in our group at the University of Wrocław in 2022. His journey in the world of physics started back in 2014 with his bachelor studies at the Aristotle University of Thessaloniki, Greece, where his main field of study was Theoretical Particle Physics. Shortly after graduating, he enrolled on the "Subatomic Particle Physics and Technological Applications" MSc course at the same university, where he studied in depth Quantum Field Theory and Standard Model Physics along with Theoretical Cosmology. During these past two years, he conducted research on Inflationary Cosmology and the Swampland, resulting in two papers published in scientific journals and two speeches in international conferences.
Luca Scala
PhD student
Period:
01.10.22 - now
E-Mail:
Office:
444
Luca joined the group in 2022 with a master's degree in physics. Following a course of study in theoretical physics at the University of Naples "Federico II", he graduated in 2018 with a thesis on wave propagation in continuum mechanics. Later on, in 2021 he completed his master graduating with full marks with his thesis on localizability in noncommutative spacetimes, dealing in particular with the well-known $\kappa$ -Minkowski and the new $\rho$ -Minkowski models. In 2022, he was awarded a three-month junior fellowship under the project "Agency-dependent spacetime and spacetime-dependent agency", funded by the Silicon Valley Community Foundation. In this time, he push the analysis of his previous results further and published an article with Prof. Fedele Lizzi and Prof. Patrizia Vitale on localization and observers in $\rho$ -Minkowski spacetime on Physical Review D.
Alex Swash
PhD student
Period:
01.10.23 - now
E-Mail:
Office:
444
Alex Swash enrolled at KU Leuven, driven by his passion for theoretical physics after completing his bachelor's degree in physics at UCLouvain in 2021. During his time at KU Leuven, he gained international experience through an Erasmus exchange at Uppsala University in Sweden. His academic journey culminated in a Master's degree in Theoretical Physics, with a thesis on flux compactifications that explored scale separation using tools from generalised geometry. Now, having graduated from Leuven in 2022, he is poised to embark on his PhD studies with our research group at the University of Wrocław.

Former Members

Tadeusz Adach (01.10.22-05.09.23), details
Tadeusz Adach
Master's student
Period:
01.10.22 - 05.09.23
E-Mail:
Tadeusz is currently enrolled in our institute's master's program on theoretical physics and is working towards his degree in our group. From previous studies, he holds an engineer's degree in computer science.

Mugshots

Special thanks to all the other PhD students in our Institute for helping us taking these group photos.

May 16th 2023, from left: Tadeusz, Luca, Falk, David, Achilles

December 5th 2023, from left: Achilles, Alex, Eric, Falk, David, Luca

Vacancies

UWr It would be great if you could join our team at the University of Wrocław (UWr)! The UWr is one of the leading universities in Poland, currently teaching over 26,000 students and around 1,300 doctoral students across ten faculties. It is situated on the banks of the Oder River in the city of Wrocław. With more than 130,000 students, Wrocław is one of the most youth-oriented cities in the heart of Europe. Our department offers a specialised master's course in theoretical physics with a large variety of advanced lectures (also available to PhD students) that prepare our students ideally to contribute to cutting edge research.

Please find below all our vacancies and do not hesitate to contact me in case of any questions.

Postdocs

There are currently no new openings for postdocs in our group. However, we encourage you to apply for postdoc grants with us. More details can be found below.

PhD students

Currently, we have no new openings for PhD students.

Master students

If you are interested in mathematical physic and want to apply it to actual research problems, you might consider writing your master thesis in our group. A solid background in Quantum Field Theory and General Relativity is an advantage, but even more important is that you are motivated and excited about the questions we approach in our group. If this is the case, please reach out to me, and I am sure we will find a project well suited to your interests and abilities.

Fellowships

If you want to join our group as a postdoc, you might also consider applying for an individual fellowship:

SONATINA is a programme from the National Science Center to researchers who got their PhD degree within 3 years prior to the submission of proposals or will have their PhD by 30 June of the year referred to in the call documents. It provides funding for up to three years. Competitions usually start mind of December and close mind March.
The Ulam NAWA Programme supports postdoc research from 6 month to 2 year. Competitions usually open in early February and close in early May. If you have a seal of excellence from a previous application for a Marie-Curie Fellowship (see below), there is a fast track and you might especially consider applying.
Marie-Curie European Postdoctoral Fellowships also provide ideal working conditions. Moreover, even if your proposal is not funded, you can still obtain a seal of excellence that helps you get funding from other sources. The call usually opens in June and closes in October.

We are very happy to help you with applications for any of these grants (and of course also other grants if you found something else which is suitable for you). If you are interested, just send me an email to .

Previous Competitions

We already concluded the two competitions

Two PhD positions, announcement, poster, successful candidates Achilles Gitsis and Luca Scala
Postdoc position, announcement, poster, successfull candidate Eric Lescano
PhD position, announcement, poster, successfull candidate Alex Swash