## Tesi etd-06272018-195402 |

Thesis type

Tesi di laurea magistrale

Author

FERRERO, PIETRO

URN

etd-06272018-195402

Title

On the Lagrangian formulation of gravity as a double copy of two Yang-Mills theories

Struttura

FISICA

Corso di studi

FISICA

Supervisors

**relatore**Dott. Francia, Dario

Parole chiave

- scattering amplitudes
- noether procedure
- gauge symmetry
- color-kinematics duality

Data inizio appello

19/07/2018;

Consultabilità

Completa

Riassunto analitico

Yang-Mills gauge theories and Einstein's General Relativity represent the main pillars on which our understanding of the fundamental interactions is presently based. Although originally formulated on account of completely independent intuitions and procedures, many connections have been later uncovered between gauge theories and gravity, stemming in particular from the inspection of scattering amplitudes in the two theories. In addition to the long-known KLT relations new correspondences were recently discovered, the so-called double-copy relations, eventually leading to recognize that, with some provisos, gravity can be understood as a suitably defined "square'' of two Yang-Mills theories. While being essentially a theorem at tree level, this insight has been more recently extended to loop-level scattering amplitudes and to classical solutions, while still being unclear both at the Lagrangian level and in its ultimate geometrical meaning.

In this Thesis we investigate the possibility of a Lagrangian formulation of this correspondence between gauge theories and gravity, focusing on the non-supersymmetric case, in which the gravitational multiplet resulting from the product of two spin-one fields also contains a two-form field and a dilaton. To this end, we exploit the definition of "double-copy field'' given by Duff et al. in order to build a quadratic Lagrangian, which has a neat interpretation as the "square'' of two Yang-Mills quadratic Lagrangians, while also discussing its geometrical meaning. The free theory is then extended to the interacting level by means of the Noether procedure, building its off-shell cubic vertices. The interactions allowed by the gauge symmetry at the cubic level contain a sector which reproduces the results of the double copy for the three-point amplitudes, while also possessing a number of notable features. In particular, the resulting Lagrangian is invariant under a twofold Lorentz symmetry and is equivalent, up to suitable field redefinitions, to the so-called N=0 Supergravity at the cubic level, which provides the natural outcome of the double copy of two pure Yang-Mills theories. Last, we discuss the deformation to the gauge transformation of the fields in the gravitational multiplet which is determined from the Noether procedure. At this level we observe the need to modify the definition of the scalar and of the graviton fields in terms of the double-copy field by also allowing for quadratic terms amenable, as we also highlight, of a tantalizing geometrical interpretation.

In this Thesis we investigate the possibility of a Lagrangian formulation of this correspondence between gauge theories and gravity, focusing on the non-supersymmetric case, in which the gravitational multiplet resulting from the product of two spin-one fields also contains a two-form field and a dilaton. To this end, we exploit the definition of "double-copy field'' given by Duff et al. in order to build a quadratic Lagrangian, which has a neat interpretation as the "square'' of two Yang-Mills quadratic Lagrangians, while also discussing its geometrical meaning. The free theory is then extended to the interacting level by means of the Noether procedure, building its off-shell cubic vertices. The interactions allowed by the gauge symmetry at the cubic level contain a sector which reproduces the results of the double copy for the three-point amplitudes, while also possessing a number of notable features. In particular, the resulting Lagrangian is invariant under a twofold Lorentz symmetry and is equivalent, up to suitable field redefinitions, to the so-called N=0 Supergravity at the cubic level, which provides the natural outcome of the double copy of two pure Yang-Mills theories. Last, we discuss the deformation to the gauge transformation of the fields in the gravitational multiplet which is determined from the Noether procedure. At this level we observe the need to modify the definition of the scalar and of the graviton fields in terms of the double-copy field by also allowing for quadratic terms amenable, as we also highlight, of a tantalizing geometrical interpretation.

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