Are all identically conserved geometric tensors metric variations of actions? A status report

Creators: Deser, S.; Pang, Y.

Abstract

Noether's theorem, that local gauge variations of gauge invariant actions are identically conserved (more tautologically, that gauge variations of gauge invariants vanish) was established a century ago. Its converse, in the geometric context: are all identically conserved local symmetric tensors variations of some coordinate invariant action? remains unsolved to this day. We survey its present state and discuss some of our concrete attempts at a solution, including a significant improvement. For notational simplicity, details are primarily given in D = 2, but we discuss generic D as well.

Additional Information

© 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. Received 14 November 2018, Revised 16 January 2019, Accepted 6 February 2019, Available online 8 February 2019. We thank Andrew Waldron for his useful suggestions in the early stages of this endless saga. The work of S.D. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. The work of Y.P. is supported by a Newton International Fellowship of the UK Royal Society.

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