Newton-Cartan gravity and torsion

Eric Bergshoeff*, Athanasios Chatzistavrakidis, Luca Romano, Jan Rosseel

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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We compare the gauging of the Bargmann algebra, for the case of arbitrary torsion, with the result that one obtains from a null-reduction of General Relativity. Whereas the two procedures lead to the same result for Newton-Cartan geometry with arbitrary torsion, the null-reduction of the Einstein equations necessarily leads to Newton-Cartan gravity with zero torsion. We show, for three space-time dimensions, how Newton-Cartan gravity with arbitrary torsion can be obtained by starting from a Schrodinger field theory with dynamical exponent z = 2 for a complex compensating scalar and next coupling this field theory to a z = 2 Schrodinger geometry with arbitrary torsion. The latter theory can be obtained from either a gauging of the Schrodinger algebra, for arbitrary torsion, or from a null-reduction of conformal gravity.

Original languageEnglish
Article number194
Number of pages20
JournalJournal of High Energy Physics
Issue number10
Publication statusPublished - 27-Oct-2017


  • Classical Theories of Gravity
  • Space-Time Symmetries

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