Abstract
We examine a two parameter family of gravitational actions which contains higher-derivative terms. These are such that the entire action is invariant under corrected T-duality rules, which we derive explicitly. Generically this action does not describe low energy string backgrounds except for isolated choices for the parameters. Nevertheless, we demonstrate that in this theory the entropy and the temperature of generic non-extremal black hole solutions are T-duality invariant. This further supports the idea put forward in our previous work that T-duality might provide physical equivalences beyond the realm of string theory.
Highlights
Things become less clear when higher-derivative corrections are introduced since, for instance, the entropy ceases to be given by the event horizon area. Their entropy and surface gravity, remain invariant under T-duality when these corrections are included? One may be tempted to answer that this is guaranteed by the very fact that these corrections to the low-energy effective action arise from a sigma model, and T-duality is an exact discrete symmetry associated to its target space
In spite of this observation, albeit T-duality constrains the possible higher-derivative terms in the action [4], there is still room for at least a two-parameter family of fourderivative T-dual invariant theories [5] — building up on earlier work [6] — which includes but goes beyond String Theory. This brings about a possible additional puzzle: what is the effect of T-duality when acting on the non-stringy black hole members of this family? Does T-duality invariance of, say, their entropy and temperature hold only for those black holes solving the equations of motion of low-energy string theory? It is natural to expect the sigma model origin of the latter to be a crucial aspect behind the result
Within the framework of so-called Double Field Theory [9], a very fruitful formalism allowing to build low-energy effective actions which are symmetric under T-duality by construction, Marques and Nunez [5] recently wrote a two-parameter family of theories governed by the generalized Bergshoeff-de Roo [10] action: IBdR =
Summary
We explain how to apply T-duality in the generalized Bergshoeff-de Roo action (1.1). We need to obtain the leading order transformation of the (torsionful) Lorentz connection under T-duality in order to later find their (a, b)-corrected rules. These can be achieved by writing Ω(M±A) B in terms of reduced fields that are transformed as in (2.7). All vielbeins of GMN which differ only in (EM A)(1) are related by Lorentz transformations of the form δAB + O(a, b)ΛAB, which are symmetries of the equations of motion to the order we are working This property follows because the only parts in the action which are not Lorentz covariant are the Chern-Simons terms appearing in H (1.2), but the compensating modification of BMN will be O(a, b) and negligible.
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