Duality invariance and higher derivatives

T duality and Wald entropy formula in the Heterotic Superstring effective action at first-order in α′

“…This requires a more general toroidal compactification of the action along the lines of the one recently obtained in ref. [9], including YM fields and closer to the Bergshoeff-de Roo formulation [58]. It is also necessary to prove the first law of black hole mechanics for the Heterotic Superstring effective action in order to make sure that the Iyer-Wald prescription can be unambiguously JHEP10(2020)097…”

“…8 Charges related to Kaluza-Klein momentum and charges related to the winding number along the compact direction should be interchanged. 9 That is, with fields related by the Buscher rules. 10 At zeroth-order in α , the Heterotic Superstring effective action only describes the so-called common sector of Neveu-Schwarz-Neveu-Schwarz fields, so the Buscher rules are just those found by Buscher.…”

“…11 As a matter of fact, they have partially re-derived several times [43,44]. Other studies of the effect of α corrections on T duality and O(d, d) transformations in toroidal compactifications, sometimes in extended set-ups (such as Double Field Theory) can be found [9,[45][46][47][48][49]. 12 It follows trivially from the invariance of the lower-dimensional string metric and dilaton under T duality that the zeroth-order in α temperature and entropy (the area) are also T duality invariant.…”

“…2 A toroidal compactification to first order in α but with no Yang-Mills fields has been recently constructed in ref. [9]. The toroidal compactification with only Abelian Yang-Mills fields (which occur at first order in α ) and no terms involving the torsionful spin connection (so the 10-dimensional action is that of N = 1, d = 10 supergravity coupled to Abelian vector supermultiplets) was carried out in [10].…”

Generalized dualities and higher derivatives

“…Looking for higher order corrections to generalized U-dualities is out of reach at the moment, because these corrections are not even known in the Abelian case. There are promising steps in this direction [116][117][118], systematics in the writing and counting of interactions is crucial [119] because higher derivatives appear in maximal supergravity at order α 3 , and so even the simplest corrections are hard to handle. Still, there is at the moment no higher derivative formulation of Exceptional Field Theory [120] nor Type II DFT [121,122] (for a review see [123]), but generalized JHEP10(2020)002…”