# Exceptional Quantum Gravity

The unification of quantum mechanics and general relativity is one the greatest challenges of contemporary theoretical physics. The need for such a theory is most pressing for the resolution of black hole singularities and the Big Bang, but it is equally crucial to the search for a consistent UV completion of the Standard Model of Particle Physics and the unification of the fundamental interactions.

The group tackles this problem from a new perspective, bringing together very different strands of development: on the one hand, by paying particular attention to recent advances in our understanding of cosmological singularities and the evidence for novel infinite-dimensional duality symmetries near the singularity that has emerged in supergravity and string theory, and to recent progress in formulating ‘exceptional geometries’ transcending Riemannian geometry. On the other hand, we are exploiting insights from modern canonical quantisation and related techniques as well as sophisticated mathematical tools (such as e.g. the theory of automorphic representations) towards a better understanding of the basic degrees of freedom and the dynamics of quantum space-time.

The main focus of the Exceptional Quantum Gravity Research Group is the maximally extended exceptional hyperbolic Kac–Moody symmetry E10, whose uniquely distinguished status makes it a prime candidate symmetry for unifying the known dualities of string and M theory, and its 'maximal compact' subgroup K(E10) generalizing the so-called R symmetries of extended supergravity theories. Amongst other goals, this symmetry based ansatz is hoped to lead to a conceptually precise scenario of emergent (quantum) space and time near the cosmological singularity, and to an explanation of the fermionic structure of the Standard Model, with 48 quarks and leptons. Equally important, it will follow up on considerable evidence that these novel infinite-dimensional duality symmetries can supersede supersymmetry in providing a new guiding principle for unification.

Consequently, the principal goals of the group’s research are to explore

- how these symmetries can define a theory of quantum gravity, with emergent space-time and matter,
- how they act on its fundamental degrees of freedom, and how known symmetry concepts (such as general covariance) can emerge from such a description,
- what the special features are of the quantised theory, and what role quantization should play in explaining emergent phenomena, and
- whether and how this ansatz can explain observed features of the Standard Model of particle physics, in particular its fermionic sector, and what new physical predictions can be derived from it.

## Research Highlights of the ERC Group

[1] E. Malek, H. Samtleben and H. Nicolai:

"Tachyonic Kaluza-Klein modes and the AdS swampland conjecture"

e-Print: 2005.07713 [hep-th], submitted to JHEP

[2] K.A. Meissner and H. Nicolai,

"Superheavy Gravitinos and Ultra-High Energy Cosmic Rays",

JCAP09(2019)041, e-print: 1906.07262[astro-ph.HE]

[3] A. Kleinschmidt, H. Nicolai and A. Vigano,

"On spinorial representations of involutory subalgebras of Kac-Moody algebras",

to appear in: Valery A. Gritsenko, Vyacheslav P. Spiridonov: Partition Functions and Automorphic Forms

e-print: 1811.11659[hep-th]

[4] K.A. Meissner and H. Nicolai,

"Planck Mass Charged Gravitino Dark Matter",

Phys. Rev. D100 (2019) 3,035001, e-print: 1809.01441[hep-ph]

[5] K. A. Meissner and H. Nicolai

"Standard Model Fermions and Infinite-Dimensional R-Symmetries",

Phys. Rev. Lett. 121 (2018) 9,091601, e-print: 1804.09606[hep-th]

[6] L.T. Kreutzer

"Canonical analysis of E6(6)(R) invariant five dimensional (super-)gravity"

e-print: 2005.13553 [hep-th]

[7] E. Malek and D. C. Thompson

"Poisson-Lie U-duality in Exceptional Field Theory"

J. High Energ. Phys. 04 (2020) 058, e-print:1911.07833 [hep-th]

[8] E. Malek and H. Samtleben

"Kaluza-Klein Spectrometry for Supergravity"

Phys. Rev. Lett. 124, 101601

[9] D. Butter, F. Ciceri and B. Sahoo

"N=4 conformal supergravity: the complete actions"

J. High Energ. Phys. 01 (2020) 029

[10] M. Henneaux, V. Lekeu and A. Leonard

"A note on the double dual graviton"

J. Phys. A 53, 1 (2019)

[11] A. Coimbra

"Higher curvature Bianchi identities, generalised geometry and $L_{∞}$ algebras"

Phys. Rev. D 100, 106001

[12] E. Malek, H. Samtleben, V. V. Camell

"Supersymmetric AdS7 and AdS6 vacua and their consistent truncations with vector multiplets"

J. High Energ. Phys. 2019, 88 (2019)

[13] D. Luest, E. Malek, E. Plauschinn and M. Syvari

"Open-String Non-Associativity in an R-flux Background"

J. High Energ. Phys. 2020**, **157 (2020)

[14] V. Lekeu and A. Leonard

"Prepotentials for linearized supergravity"

Class. and Quantum Gravity 36, Number 4

[15] L. Casarin, H. Godazgar and H. Nicolai

"Conformal anomaly for non-conformal scalar fields"

Phys. Lett. B, 787 94 (2018)

[16] M. Henneaux, V. Lekeu, A. Leonard, J. Matulich and S. Prohazka

"Three-dimensional conformal geometry and prepotentials for four-dimensional fermionic higher-spin fields"

J. High Energ. Phys. 2018**, **156 (2018)

[17] G. Bossard, F. Ciceri, G. Inverso, A. Kleinschmidt and H. Samtleben

"E9 exceptional field theory I. The potential"

J. High Energ. Phys. 2019**, **89 (2019)

[18] M. Broccoli and A. Viganò

"Electromagnetic self-force in curved spacetime: New insights from the Janis-Newman algorithm"

Phys. Rev. D 98, 084007 (2018)

[19] R. Kallosh, H. Nicolai, R. Roiban and Y. Yamada

"On quantum compatibility of counterterm deformations and duality symmetries in N ≥ 5 supergravities"

J. High Energ. Phys. 2018**, **91 (2018).