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Published December 2018 | Submitted + Published
Journal Article Open

Motives and periods in Bianchi IX gravity models


We show that, when considering the anisotropic scaling factors and their derivatives as affine variables, the coefficients of the heat-kernel expansion of the Dirac–Laplacian on SU(2) Bianchi IX metrics are algebro-geometric periods of motives of complements in affine spaces of unions of quadrics and hyperplanes. We show that the motives are mixed Tate and we provide an explicit computation of their Grothendieck classes.

Additional Information

© 2018 Springer Science+Business Media B.V., part of Springer Nature. Received: 21 January 2018; Revised: 30 April 2018; Accepted: 1 May 2018; Published online: 7 May 2018. The second author acknowledges support from the Marie Curie/SER Cymru II Cofund Research Fellowship 663830-SU-008. The third author acknowledges support from NSF Grant DMS-1707882, NSERC Discovery Grant RGPIN-2018-04937 and from the Perimeter Institute for Theoretical Physics.

Attached Files

Published - Fan2018_Article_MotivesAndPeriodsInBianchiIXGr.pdf

Submitted - 1709.08082.pdf


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