Higher Spin Gravity and Generalized Spacetime Geometry

Projektinformationen

High-Spin-Grav

ID Finanzhilfevereinbarung: 694089

DOI

10.3030/694089

Projekt abgeschlossen

EK-Unterschriftsdatum 21 April 2016

Startdatum 1 Oktober 2016

Enddatum 30 September 2021

Finanziert unter

• EXCELLENT SCIENCE - European Research Council (ERC)

Gesamtkosten

€ 1 841 868,00

EU-Beitrag

€ 1 841 868,00

Koordiniert durch

UNIVERSITE LIBRE DE BRUXELLES
Belgium

Periodic Reporting for period 4 - High-Spin-Grav (Higher Spin Gravity and Generalized Spacetime Geometry)

Berichtszeitraum: 2021-04-01 bis 2021-09-30

Zusammenfassung vom Kontext und den Gesamtzielen des Projekts

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 – 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.

Major progress has been performed on all the topics (i)-(v). The project has been successful not only in terms of its scientific output, resulting in numerous publications in leading journals and presentations in seminars and conferences, but also through its training dimension with 14 PhD students and postdoctoral fellows hired during the corresponding period.

Arbeit, die ab Beginn des Projekts bis zum Ende des durch den Bericht erfassten Berichtszeitraums geleistet wurde, und die wichtigsten bis dahin erzielten Ergebnisse

The work pursued during the period of the project made several major advances on the 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. This new approach not only crucially resolves long-standing tensions between null infinity and spatial infinity but it also inspires new lines of investigation and reveals unanticipated structures at infinity (nonlinear asymptotic symmetry algebras).

Third, a profound original insight on duality symmetry for higher spin gauge fields (a "hidden symmetry") that has been gained, where action principles explicitly invariant under duality have been constructed.

Fourth,higher spin charges associated with "large" ("improper") higher spin gauge transformations have been defined in three spacetime dimension by elucidating the asymptotic structure of the fields at infinity.

The work has resulted in 59 publications in leading peer-reviewed journals (plus 2 in press), as well as in a great number of seminars in foreign universities and of presentations at international conferences and at doctoral schools. A monograph "The cosmological singularity" co-authored with V. Belinski has been published by Cambridge University Press.

Fortschritte, die über den aktuellen Stand der Technik hinausgehen und voraussichtliche potenzielle Auswirkungen (einschließlich der bis dato erzielten sozioökonomischen Auswirkungen und weiter gefassten gesellschaftlichen Auswirkungen des Projekts)

The above achievements are results that go beyond the state of the art. Major difficulties have been overcome, pioneering new approaches to important questions such as the asymptotic structure of gravity or actions for self-dual fields.

While the project itself is terminated and has fulfilled its planned goals, it raises many new exciting questions that could not have been anticipated five years ago and opens many new lines of investigation with great promise.

Asymptotic structure of spacetime (spacelike infinity i°)