Higher Derivative Corrections, Dimensional Reduction and Ehlers Duality

Details Higher Derivative Corrections, Dimensional Reduction and Ehlers Duality Higher Derivative Corrections, Dimensional Reduction and Ehlers Duality

2007-06-12

arxiv.org/abs/0706.1769v3

JHEP 0709:103,2007

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, uses JHEP3.cls; v3: minor corrections, final version published in JHEP

Scientific paper

10.1088/1126-6708/2007/09/103

Motivated by applications to black hole physics and duality, we study the effect of higher derivative corrections on the dimensional reduction of four-dimensional Einstein, Einstein Liouville and Einstein-Maxwell gravity to one direction, as appropriate for stationary, spherically symmetric solutions. We construct a field redefinition scheme such that the one-dimensional Lagrangian is corrected only by powers of first derivatives of the fields, eliminating spurious modes and providing a suitable starting point for quantization. We show that the Ehlers symmetry, broken by the leading $R^2$ corrections in Einstein-Liouville gravity, can be restored by including contributions of Taub-NUT instantons. Finally, we give a preliminary discussion of the duality between higher-derivative F-term corrections on the vector and hypermultiplet branches in N=2 supergravity in four dimensions.

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