Higher Derivative Corrections, Dimensional Reduction and Ehlers Duality

TL;DR

This paper investigates how higher derivative corrections influence the dimensional reduction of gravity theories, restoring symmetries like Ehlers duality through instanton contributions, with implications for black hole physics and supergravity dualities.

Contribution

It introduces a field redefinition scheme to handle higher derivative corrections and demonstrates the restoration of Ehlers symmetry via Taub-NUT instantons.

Findings

Higher derivative corrections break Ehlers symmetry in Einstein-Liouville gravity.

A field redefinition scheme isolates first-derivative terms, aiding quantization.

Ehlers symmetry can be restored by including instanton effects.

Abstract

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.