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arXiv · 1006.3762

Non-relativistic metrics from back-reacting fermions

Ling-Yan Hung·Dileep P. Jatkar·Aninda Sinha
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Abstract

It has recently been pointed out that under certain circumstances the back-reaction of charged, massive Dirac fermions causes important modifications to AdS_2 spacetimes arising as the near horizon geometry of extremal black holes. In a WKB approximation, the modified geometry becomes a non-relativistic Lifshitz spacetime. In three dimensions, it is known that integrating out charged, massive fermions gives rise to gravitational and Maxwell Chern-Simons terms. We show that Schrodinger (warped AdS_3) spacetimes exist as solutions to a gravitational and Maxwell Chern-Simons theory with a cosmological constant. Motivated by this, we look for warped AdS_3 or Schrodinger metrics as exact solutions to a fully back-reacted theory containing Dirac fermions in three and four dimensions. We work out the dynamical exponent in terms of the fermion mass and generalize this result to arbitrary dimensions.

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Ling-Yan Hung, Dileep P. Jatkar, Aninda Sinha. 2010-06-29. Non-relativistic metrics from back-reacting fermions. https://doi.org/10.1088/0264-9381%2F28%2F1%2F015013

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