From Newton’s gravitational law to electroweak unification, the idea that the complexity of phenomena results from the infinite possibilities of manifestation of a few relatively simple laws has successfully informed theoretical research for decades. Theories based on local symmetries cover the range of known interactions, including electroweak and strong forces, as well as Einstein–Hilbert’s gravity, the latter based on the mathematical incarnation of the equivalence principle. The possibility of a complete quantum description of the gravitational force, on the other hand, remains one of the beacons of theoretical investigation.

The project is centered on the study of new, unexpected symmetries that emerge in various  approaches aimed at exploring the meaning of gravity in the quantum regime, and it is divided into three main strands:

    1. The so-called “double copy relations’’ that point to the existence of surprising correspondences between interactions of completely different origin and meaning, such as subnuclear forces and gravitation. They show that gravity can be interpreted as the product of two Yang–Mills theories, at least in the sense that multiplying two scattering amplitudes in the gauge theory setup reproduces an element of the gravitational S-matrix. These relationships, now fully understood and formalized at tree level, extend to cover a vast range of options including theories with scalar particles only, nonlinear sigma models, and supersymmetric models, to form a multiplicative table of unexpected correspondences [1]. However, their geometric, off-shell understanding at the Lagrangian level, which would allow in particular exploration and test both existence and meaning of double copy relations at the level of quantum corrections, is still missing [2].
    2. The exploration of the links between infrared properties of gauge theories, scattering amplitudes with emission of zero-mass particles in the “soft’’ limit, and asymptotic symmetries for Yang–Mills theories and for gravity [3], as well as for theories including arbitrary spin fields [4,5]. This type of investigation takes up and updates a long tradition of studies on the infrared behavior of QED amplitudes dating back to at least the 1950s. New motivations result in the possibility of associating directly observable quantities (so-called “memory’’ effects) with local transformations and, on a more speculative level, in some conjectures on the potential role of such asymptotic symmetries in determining the fate of information in the process of creation and evaporation of black holes. In addition, there are indications suggesting that asymptotic symmetries may be instrumental in defining and understanding holographic correspondences on asymptotically flat spaces [3]. Moreover, for scattering amplitudes involving string states in the very high energy limit, where the corresponding masses should be negligible, the emergence of asymptotic symmetries for high-spin states should provide useful signatures of the corresponding underlying geometry [4,5].
    3. The formulation of high-spin gauge theories, candidates to describe the high-energy limit of String Theory. The known fundamental interactions match the low-energy spectrum of String Theory, most of the excitations of which, however, are made up of massive particles of high spin. The latter are crucial to ensuring the soft ultraviolet behavior of string amplitudes, instrumental in candidating String Theory as an ultraviolet completion of General Relativity. On the other hand, the masses of these infinite excitations seem to emerge from a complex symmetry-breaking mechanism whose details are not yet understood. Massive resonances of spin greater than one (or greater than ½, in the case of fermions), however, are common in hadronic physics. Conversely, in systems of this type with zero mass, profound difficulties are encountered associated with the corresponding gauge symmetry. It is therefore natural to ask which symmetries (and thus which interactions) can actually regulate the behavior of massive high spin states at very high energies, how their breaking occurs and what is the meaning of these broken symmetries, and of the corresponding interactions, in terms of geometry [6,7,8]. This line of investigation aims both at clarifying the geometric underpinnings of String Theory and, more generally, at shaping the actual theoretical and phenomenological status of a whole class of possible UV-complete theories of gravity.
  • [1] Z. Bern, J.J. Carrasco, M. Chiodaroli, H. Johansson and R.Roiban,“The Duality Between Color and Kinematics and its Applications,” [arXiv:1909.01358 [hep-th]].
  • [2] P. Ferrero, “On the Lagrangian formulation of gravity as a double copy of two Yang-Mills theories,” Master Thesis, Scuola Normale Superiore and Università di Pisa, 2018. Supervisor: D. Francia ETD
  • [3] A.Strominger, “Lectures on the Infrared Structure of Gravity and Gauge Theory,” Princeton University Press 2018 [arXiv:1703.05448 [hep-th]].
  • [4] A. Campoleoni, D. Francia and C.Heissenberg, “On higher-spin supertranslations and superrotations,” JHEP 05 (2017), 120 [arXiv:1703.01351 [hep-th]].
  • [5] A. Campoleoni, D. Francia and C. Heissenberg,“Asymptotic Charges at Null Infinity in Any Dimension,” Universe 4 (2018) no.3, 47 [arXiv:1712.09591 [hep-th]].
  • [6] X. Bekaert, S. Cnockaert, C. Iazeolla and M. A. Vasiliev,“Nonlinear higher spin theories in various dimensions,” [arXiv:hep-th/0503128 [hep-th]].
  • [7] M. Gaberdiel, M. A. Vasiliev (eds) “Higher spin theories and holography’’ J Phys A 46 (2013) 21
  • [8] D. Francia, G. Lo Monaco and K. Mkrtchyan, “Cubic interactions of Maxwell-like higher spins,” JHEP 04 (2017), 068 [arXiv:1611.00292 [hep-th]].

Dario Francia

  • Andrea Campoleoni — Mons U and FNRS
  • Pietro Ferrero  — Oxford U
  • Carlo Heissenberg  —  Nordita and Royal Institute of Technology, Stockholm and Uppsala U
  • Karapet Mkrtchyan — Scuola Normale Superiore, Pisa
From the Standard Model of Fundamental Interactions to Einstein’s Gravity, our best understanding of the laws underlying physical phenomena is based on the identification of the corresponding symmetries. The challenge posed by quantum gravity requires the exploration of new and richer structures.