Annals of Mathematical Sciences and Applications

Volume 2 (2017)

Number 1

Higher-dimensional supertranslations and Weinberg’s soft graviton theorem

Pages: 69 – 94

DOI: https://dx.doi.org/10.4310/AMSA.2017.v2.n1.a2

Authors

Daniel Kapec (Center for the Fundamental Laws of Nature, Harvard University, Cambridge, Massachusetts, U.S.A.)

Vyacheslav Lysov (Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, Calif., U.S.A.)

Sabrina Pasterski (Center for the Fundamental Laws of Nature, Harvard University, Cambridge, Massachusetts, U.S.A.)

Andrew Strominger (Center for the Fundamental Laws of Nature, Harvard University, Cambridge, Massachusetts, U.S.A.)

Abstract

Asymptotic symmetries of theories with gravity in $d = 2m + 2$ spacetime dimensions are reconsidered for $m \gt 1$ in light of recent results concerning $d = 4$ BMS symmetries. Weinberg’s soft graviton theorem in $2m+2$ dimensions is re-expressed as a Ward identity for the gravitational $\mathcal{S}$-matrix. The corresponding asymptotic symmetries are identified with $2m+ 2$-dimensional supertranslations. An alternate derivation of these asymptotic symmetries as diffeomorphisms which preserve finite-energy boundary conditions at null infinity and act non-trivially on physical data is given. Our results differ from those of previous analyses whose stronger boundary conditions precluded supertranslations for $d \gt 4$. We find for all even $d$ that supertranslation symmetry is spontaneously broken in the conventional vacuum and identify soft gravitons as the corresponding Goldstone bosons.

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Published 13 January 2017