## The double copy paradigm : (gauge)² = gravity ?

Gravitational physics has been related to gauge theories in a number of ways and in various guises; as for instance in one the main topics of the current mainstream of high-energy theoretical physics, namely the holographic principle realized in terms of the AdS/CFT correspondence, whose amazing developments are affecting in depth our understanding of both gauge and gravity theories.

This project is focused on a research venue which can be summarized with the motto: “gravity = Yang-Mills x Yang-Mills”.

This may look as a provocative and unlikely proposal, since Einstein’s General Relativity (GR) and Yang-Mills (YM) gauge theories are very different theories in many regards, such as their symmetries and the fundamental degrees of freedom they take into account : while GR regards gravity as the very dynamics of the spacetime, YM theories are at the foundation of the Standard Model (SM) of particle physics, describing strong, weak and electromagnetic forces. Moreover, while the SM is renormalizable, a consistent theory of quantum gravity is not yet formulated.

Despite such essential differences, nowadays a tantalizing amount of evidence has been cumulated in relating gravity, at least within certain regimes, to the “square” of YM theory. This evidence relies on a Lie-algebraic structure of certain kinematic building blocks in the diagrammatic presentations of gauge theory scattering amplitudes : they can be rearranged to express the integrands of gravity amplitudes as double copies of the ones of gauge theory.

All this led to conjecture that, to all orders in perturbation theory, the on-mass-shell momentum-space scattering amplitudes of certain gravity theories are the “double-copy”, in a precise sense, of gluon scattering amplitudes belonging to two independent YM theories. A prototypical example (which is also the simplest one, due to the high degree of symmetry) is provided by N = 8 supergravity as the “product” of two N = 4 YM theories.

In recent years, the double copy paradigm has been extended beyond amplitudes in a variety of directions, see e.g. [1],[2]. In particular, the double copy has been formulated at the level of off-shell linearized supermultiplets in [3]-[5]. Furthermore, a double copy structure relating classical solutions of gauge and gravity theories was identified, raising hope for its application as a solution-generating technique for asymptotically-flat perturbative solutions in GR [6].

Recently, great progress has been made to unravel the double copy structure of supergravity theories in various dimensions, also highlighting the role of local supersymmetry [7]-[10].

The present research project is placed at the edge of the current efforts to shed light onto such a deep structure of gravitational theories, both at a fundamental level (unraveling new facets of quantum gravity through the investigation of the double copy within supergravity and string theory) and at a phenomenological/computational level (investigating the application of the double copy factorization in scattering amplitudes of gravitons in various contexts, such as gravitational waves).

- A. Anastasiou, L. Borsten, M. J. Duff, M. J. Hughes, S. Nagy,
*“Yang-Mills origin of gravitational symmetries”*, Phys. Rev. Lett.**113**, 231606 (2014), doi: 10.1103/PhysRevLett.113.231606. - L. Borsten, M. J. Duff,
*“Gravity as the square of Yang-Mills?”*, Phys. Scripta**90**(2015) 108012, DOI: 10.1088/0031-8949/90/10/108012. - L. Borsten, M. J. Duff, M. J. Hughes, S. Nagy,
*“Magic Square from Yang-Mills Squared”*, Phys. Rev. Lett.**112**(2014), no. 13 131601, doi: 10.1103/PhysRevLett.112.131601. - A. Anastasiou, L. Borsten, M. J. Duff, M. J. Hughes, S. Nagy,
*“A magic pyramid of supergravities”*, JHEP**1404**(2014) 178, doi: 10.1007/JHEP04(2014)178. - A. Anastasiou, L. Borsten, M.J. Duff, S. Nagy, M. Zoccali,
*“Gravity as Gauge Theory Squared: A Ghost Story”*, Phys. Rev. Lett.**121**(2018) no.21, 211601, doi: 10.1103/PhysRevLett.121.211601 - A. Luna, R. Monteiro, I. Nicholson, A. Ochirov, D. O’Connell, N. Westerberg, C. D. White,
*“Perturbative spacetimes from Yang-Mills theory”*, JHEP**1704**(2017) 069, doi: 10.1007/JHEP04(2017)069 - A. Anastasiou, L. Borsten, M.J. Duff, M.J. Hughes, A. Marrani, S. Nagy, M. Zoccali,
*“Twin supergravities from Yang-Mills theory squared”*, Phys. Rev.**D96**(2017) no.2, 026013, doi: 10.1103/PhysRevD.96.026013. - A. Anastasiou, L. Borsten, M.J. Duff, A. Marrani, S. Nagy, M. Zoccali,
*“Are all supergravity theories Yang–Mills squared?”*, Nucl. Phys.**B934**(2018) 606-633, doi: 10.1016/j.nuclphysb.2018.07.023. - A. Anastasiou, L. Borsten, M.J. Duff, A. Marrani, S. Nagy, M. Zoccali, “
*The Mile High Magic Pyramid”*, Contemp.Math.**721**(2019) 1-27, e-Print: 1711.08476 [hep-th]. - L. Borsten, M.J. Duff, A. Marrani,
*“**Twin conformal field theories”*, JHEP**03**(2019) 112, doi: 10.1007/JHEP03(2019)112.

Alessio Marrani

- Dr. Leron Borsten (Maxwell Inst. Math. Sci., Edinburgh)
- Prof. Sergio L. Cacciatori (Insubria U., Como)
- Prof. Michael J.Duff (Texas A-M U., and Imperial Coll., London)
- Dr. Silvia Nagy (Nottingham U.)