Higher Structures, Gravity and Fields

9 Jan 2023, 09:00 → 27 Jan 2023, 17:00 Europe/Berlin

02.430 (Mainz Institute for Theoretical Physics, Johannes Gutenberg University)

Many physical models possess symmetries that cannot be described by Lie algebras, but require some kind of higher structure. This applies already to p-form gauge fields, described by gerbes rather than fibre bundles. An example under active research is generalised or extended geometry — models capturing duality symmetries of gravity or supergravity, often inherited from string theory, and described in terms of differential geometry of L∞-algebras, Courant and Leibniz algebroids, QP manifolds, differential graded algebras, tensor hierarchy algebras, etc.

We organise a 3-week programme bringing together theoretical physicists and mathematicians working in the areas of gravity, dualities, extended geometry, field theory, higher homotopy structures, and other infinite-dimensional superalgebras. The overarching goal is to make progress in constructing “exotic” field theories, where conventional notions of spacetime break down, and thus traditional methods fail. These include exotic forms of gravity, extended (double and exceptional) geometry, string/M-theory and its dualities, and higher spin theories.

The common feature of these theories is the appearance of higher symmetry algebras, generalising the notion of Lie algebras. In this programme, we will bring physicists and mathematicians together working on these “higher structures” in order to better understand the fundamental structures of physical theories and develop a bootstrap based on higher structures. 

Keywords:

· gravity, including non-standard versions
· string theory / M-theory
· dualities
· extended and graded geometry
· gauge theory
· higher spin theory
· higher homotopy structures
· infinite-dimensional superalgebras

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Monday 9 January

09:00 → 10:00 registration

10:00 → 10:30 Coffee break

10:30 → 11:30 Geometric actions in gravity

Speaker: Glenn Barnich

15:00 → 15:30 Coffee break

15:30 → 16:30 Asymptotic structure of gravity with Ehlers symmetry

Speaker: Sucheta Majumdar

18:00 → 19:00 Reception: drinks and snacks at the institute

Tuesday 10 January

10:00 → 10:30 Coffee break

10:30 → 11:30 Higher-spins from higher dualisations

Speaker: Nicolas Boulanger

15:00 → 15:30 Coffee break

15:30 → 16:30 Brane wrapping in AKSZ topological field theories

Speaker: David Tennyson

Wednesday 11 January

10:00 → 10:30 Coffee break

10:30 → 11:30 Quest for Background Independence

Speaker: Ivo Sachs

15:00 → 15:30 Coffee break

15:30 → 16:30 Higher-derivative corrections and duality invariance

Speaker: Camille Eloy

19:00 → 21:00 workshop dinner

Thursday 12 January

10:00 → 10:30 Coffee break

10:30 → 11:30 Double Field Theory as the Double Copy of Yang-Mills Theory

Speaker: Olaf Hohm

15:00 → 15:30 Coffee break

15:30 → 16:30 Supergravity and Supergeometry

Speaker: Pietro Grassi

Friday 13 January

10:00 → 10:30 Coffee break

10:30 → 11:30 Presymplectic gauge PDEs and Lagrangian BV formalism beyond jet-bundles

Speaker: Maxim Grigoriev

15:00 → 15:30 Coffee break

15:30 → 16:30 Consistent Truncations and Dualities

A major application of extended geometries in supergravity is
the construction of consistent truncations. Remarkably, all this
construction's ingredients also appear in the context of generalised T-
and U-dualities. After a quick review of both concepts, I will discuss a
conjectured correspondence between consistent truncations and
generalised dualities in string and M-theory. We will prove that all
known generalised dualities give rise to consistent truncations.
Moreover, we will see evidence that after incorporating higher
derivative correction, all consistent truncations might be based on
generalised dualities.

Speaker: Falk Hassler

Monday 16 January

09:00 → 10:00 registration

10:00 → 10:30 Coffee break

10:30 → 11:30 Spinors and geometric structures

My aim will be to explain some relatively well-known (and then less-known) geometric constructions linking structures of the type appearing in double field theory to spinors. The well-known example is that of a split signature metric on a vector space together with a choice of a maximal totally null subspace as encoded by a real pure spinor. But I will also describe less-known examples when the metric together with (a unit) spinor is encoded by a collection of certain differential forms. I will describe how going up in dimension necessitates considering impure spinors, and how these bring with themselves even more interesting geometry. My plan is to end with an example in 14 dimensions, with a split signature metric, where a generic real spinor can be shown to encode the second (dynamical) metric of double field theory.

I hope to be able to make this talk interesting to anyone familiar with generalised geometry and/or double field theory.

Speaker: Kirill Krasnov

15:00 → 15:30 Coffee break

15:30 → 16:30 On the backgrounds of spinning particles

Spinning particles are models for point particles with spin degrees of freedom. They automatically feature N-supersymmetry on the worldline, with fixed albeit arbitrary N. After first quantization one obtains spin-N/2 states in the Hilbert space. Consistency conditions for second quantization, realized in the form of BRST quantization, can severely restrict the background fields in target space, putting them on-shell. In the N=2 case the target space can host a Yang-Mills gauge theory, while in N=4 it is possible to have Einstein's gravity and the NS-NS sector of Supergravity.
After explaining these passages, I will present new results involving the Ramond-Ramond fluxes (based on arXiv:2206.03243 with I. Sachs). I wish to conclude this analysis with some brief comments on almost complex structures (on-going work with O. Hulik and I. Sachs).

Speaker: Eugenia Boffo

18:00 → 19:00 Reception: drinks and snacks at the institute

Tuesday 17 January

10:00 → 10:30 Coffee break

10:30 → 11:30 Conformal (higher spin) gravity and Deformation quantization

Speaker: Evgeny Skvortsov

15:00 → 15:30 Coffee break

15:30 → 16:30 Post-Newtonian Test of Double Field Theory

Speaker: Jeong-Hyuck Park

Wednesday 18 January

10:00 → 10:30 Coffee break

10:30 → 11:30 From Lie algebra crossed modules to tensor hierarchies, and beyond

Gauging procedures in supergravity theories depart from classical gauge theories as in the former, the gauge fields take values in the fundamental representation V of the Lie algebra g of global symmetries of the system. The consistency of the theory relies on a pairing V-->g called the embedding tensor, turning V into a Leibniz algebra. As is usually met in higher gauge theories, if the gauge algebra is not Lie, it is replaced by some higher form of Lie algebras. Here, such a higher structure is materialized by a differential graded Lie algebra on a chain complex of g-modules, called the tensor hierarchy. In the present talk we explain how tensor hierarchies are genetically related to Lie algebra crossed modules.
Indeed, two such algebras V and g, together with their embedding tensor, form a triple called a Lie-Leibniz triple, of which Lie algebra crossed modules are particular cases. The canonical assignment (functor) associating to any Lie algebra crossed module its corresponding unique 2-term differential graded Lie algebra can be extended to the category of Lie-Leibniz triples, giving their associated tensor hierarchies. This shows that Lie-Leibniz triples form natural generalizations of Lie algebra crossed modules and that their associated tensor hierarchies can be considered as some kind of 'lie-ization' of the former. The "oidization" of such Lie-Leibniz triples then conjecturally opens the possibility to define the tensor hierarchies associated to Courant algebroids and G-algebroids.

Speaker: Sylvain Lavau

15:00 → 15:30 Coffee break

15:30 → 16:30 Carrollian and Galilean conformal spin-3 theories in 3d

Speaker: Iva Lovrekovic

Thursday 19 January

10:00 → 10:30 Coffee break

10:30 → 11:30 D=2 supergravity and affine exceptional field theory

Speaker: Franz Ciceri

15:00 → 15:30 Coffee break

15:30 → 16:30 2d gauged supergravity and consistent truncations

Speaker: Gianluca Inverso

19:00 → 22:00 workshop dinner

Friday 20 January

10:00 → 10:30 Coffee break

10:30 → 11:30 The most complicated way of writing D=11 supergravity

Speaker: Axel Kleinschmidt

15:00 → 15:30 Coffee break

15:30 → 16:30 Arborescent Koszul-Tate resolutions and BFV for singular coisotropic reductions

Let $I$ be an ideal in some commutative (associative) algebra $O$. Starting from resolution of $O/I$ as an $O$-module, we construct a Koszul-Tate resolution for this quotient, i.e.\ a graded symmetric algebra over $O$ with a differential which provides simultaneously a resolution as an $O$-module. This algebra resolution has a beautiful structure of a forest of decorated trees and is related to an $A_\infty$ algebra on the original module resolution.

Considering $O$ to be a Poisson algebra and $I$ a finitely generated Poisson subalgebra, we use the above construction to obtain the corresponding BFV formulation. Its cohomology at degree zero is proven to coincide with the reduced Poisson algebra $N(I)/I$, where $N(I)$ is the normaliser of $I$ inside $O$, thus generalising ordinary coisotropic reduction to the singular setting. As an illustration we use the example where $O$ consists of functions on $T^*(\R^3)$ and $I$ is the ideal generated by angular momenta.

This is joint work with Aliaksandr Hancharuk and, in part, with Camille Laurent-Gengoux.

Speaker: Thomas Strobl

Monday 23 January

09:00 → 10:00 registration

10:00 → 10:30 Coffee break

10:30 → 11:30 Extended geometry and restricted associativity

Speaker: Jakob Palmqvist

15:00 → 15:30 Coffee break

15:30 → 16:30 Algebraic structures in the pure spinor superfield formalism

Speaker: Ingmar Saberi

18:00 → 19:00 Reception: drinks and snacks at the institute

Tuesday 24 January

10:00 → 10:30 Coffee break

10:30 → 11:30 A new consistent limit of 11D supergravity

Speaker: Eric Bergshoeff

15:00 → 15:30 Coffee break

15:30 → 16:30 Systematics of consistent truncations

Speaker: Michela Petrini

18:00 → 18:30 Branes and kappa symmetry: a supergeometric insight

Speaker: Carlo Alberto Cremonini

Wednesday 25 January

10:00 → 10:30 Coffee break

10:30 → 11:30 Counting moduli of flux backgrounds

Speaker: Daniel Waldram

15:00 → 15:30 Coffee break

15:30 → 16:30 Quantum space-time, torsion and gravity from quantum effects in the IIB matrix model

Speaker: Harold Steinacker

20:30 → 23:30 workshop dinner

Thursday 26 January

10:00 → 10:30 Coffee break

10:30 → 11:30 Gauge theory, higher structures and compatibility conditions

Speaker: Athanasios Chatzistavrakidis

15:00 → 15:30 Coffee break

15:30 → 16:30 G-algebroids, embedding tensors, and Poisson–Lie duality

I will describe a class of structures, known as G-algebroids, which arises as a natural generalisation of the ordinary, generalised, and exceptional tangent bundles from ordinary, generalised, and exceptional geometry, respectively. I will discuss a classification result in the exceptional case and show how to obtain the possible fluxes/twists of the bracket. In the M-theory and IIB setups, the twists organise themselves naturally into connections and covariantly constant differential forms, while in the IIA case one in particular recovers both the Romans mass and the deformation of Howe–Lambert–West. Finally, I will show how to use these algebroids to answer a question about the realisability of embedding tensors (providing a new perspective on the result of Inverso '17) and to give a joint description of the Poisson–Lie T- and U-duality. This is a joint work with M. Bugden, O. Hulik, and D. Waldram.

Speaker: Fridrich Valach

18:00 → 18:30 Palatini variation in generalized geometry and effective actions

Speaker: Branislav Jurco

Friday 27 January

10:00 → 10:30 Coffee break

10:30 → 11:30 Quantization of braided noncommutative field theories

In this talk we will shortly review the construction of noncommutative field theories via the (braided) L-infinity algebra. Then we will discuss quantization of these theories on two examples: braided scalar field theory and braided U(1) gauge theory coupled with fermions, braided electrodynamics. In the case of scalar field theory we show the absence of UV/IR mixing at one loop order, while in the braided electrodynamics the UV/IR mixing remains present at one loop order.

Speaker: Marija Dimitrijević Ćirić

15:00 → 15:30 Coffee break

15:30 → 16:30 D-branes and doubled geometry

Speaker: Richard Szabo