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Report

Teaser, summary, work performed and final results

Periodic Reporting for period 2 - High-Spin-Grav (Higher Spin Gravity and Generalized Spacetime Geometry)

Teaser

Summary

The problem of reconciling Einstein\'s theory of gravity with quantum mechanics is an outstanding challenge of modern physics. Extensions of Einstein\'s theory of gravity containing higher spin gauge fields (massless fields with spins greater than two), called ``higher spin gravity\'\', appear to be a significant element of many approaches to this problem. The objective of the project is to deepen our current understanding of higher spin gravity following five interconnected central themes that constitute its
backbone: (i) how to construct an action principle; (ii) how to understand the generalized space-time geometry invariant under the higher-spin gauge symmetry â€“ a key fundamental issue in the project; (iii) what is the precise asymptotic
structure of the theory at infinity; (iv) what is the connection of the higher spin algebras with the hidden symmetries of gravitational theories; (v) what are the implications of hypersymmetry, which is the higher-spin version of supersymmetry.

One of the motivations of the project is the connection of higher spin gravity with tensionless string theory, where massless higher spin fields are present.

Work performed

Our work made two major advances on the following objectives of the project. First, an action principle for chiral higher spin gauge fields described by tensors of mixed Young symmetry with self-dual field strengths has been explicitly built. This question is relevant to chiral maximal supersymmetry in 6 spacetime dimensions and required the development of new algebraic and geometrical tools generalizing the Cotton tensor of ordinary Riemannian geometry. Second, a major effort has been launched towards understanding the asymptotic structure of gravity at spatial infinity, putting the action and its invariance in the foreground. The identification of the infinite-dimensional symmetry group (BMS group) at spatial infinity has been successfully derived.

Final results

The above achievements, and the other results leading to published articles in peer-reviewed journals (22 in total), go beyond the state of the art. It is expected to make progress on the construction of interactions for the chiral theories described in the first point. The extension of the asymptotic analysis to higher dimensions and to higher spin gauge fields holds exciting promises.