## Final Report Summary - SYDUGRAM (Symmetries and Dualities in Gravity and M-theory)

Of all the fundamental interactions (electromagnetism, weak and strong nuclear forces, gravitation), gravity is the least understood. Despite its considerable success, Einstein theory of gravity is an unfinished revolution: it has limitations both at the microscopic scales and at the macroscopic scales. A better understanding of the gravitational interaction going beyond Einstein is therefore needed.

It is expected that one way to reach the searched-for fundamental formulation of gravity is to identify its symmetry structure. Recent work has uncovered remarkable infinite-dimensional symmetry algebras in the study of supergravities and M-theory. These symmetries, sometimes called "hidden symmetries" because they are not manifest in the original formulations, encompass the duality symmetries that have contributed so much to the spectacular progress of string theory.

The main goal of the research project was to provide new key insight onto the fundamental symmetry structure of gravity.

The project has been mostly devoted to deepen the understanding of (i) electric-magnetic duality as a dynamical symmetry of the action, (ii) the mathematical structure of the "hidden symmetries", (iii) the connection between spacetime covariance and duality, and (iv) the role of higher spin gauge fields in the physical realization of the infinite-dimensional algebras. In particular, gravitational electric-magnetic duality has been the focus of a considerable amount of investigation.

Significant progress has been achieved on all the topics (i)-(iv) listed in the previous paragraph, leading to the publication of 47 articles in refereed journals. The results were also presented at international conferences and at numerous seminars in specialized research institutions and universities.

It is expected that one way to reach the searched-for fundamental formulation of gravity is to identify its symmetry structure. Recent work has uncovered remarkable infinite-dimensional symmetry algebras in the study of supergravities and M-theory. These symmetries, sometimes called "hidden symmetries" because they are not manifest in the original formulations, encompass the duality symmetries that have contributed so much to the spectacular progress of string theory.

The main goal of the research project was to provide new key insight onto the fundamental symmetry structure of gravity.

The project has been mostly devoted to deepen the understanding of (i) electric-magnetic duality as a dynamical symmetry of the action, (ii) the mathematical structure of the "hidden symmetries", (iii) the connection between spacetime covariance and duality, and (iv) the role of higher spin gauge fields in the physical realization of the infinite-dimensional algebras. In particular, gravitational electric-magnetic duality has been the focus of a considerable amount of investigation.

Significant progress has been achieved on all the topics (i)-(iv) listed in the previous paragraph, leading to the publication of 47 articles in refereed journals. The results were also presented at international conferences and at numerous seminars in specialized research institutions and universities.