Non‐geometric fluxes in supergravity and double field theory

Abstract

In this paper we propose ten‐dimensional realizations of the non‐geometric fluxes Q and R. In particular, they appear in the NSNS Lagrangian after performing a field redefinition that takes the form of a T‐duality transformation. Double field theory simplifies the computation of the field redefinition significantly, and also completes the higher‐dimensional picture by providing a geometrical role for the non‐geometric fluxes once the winding derivatives are taken into account. The relation to four‐dimensional gauged supergravities, together with the global obstructions of non‐geometry, are discussed.

T-duality and α′-corrections

“…Understanding the role of supersymmetry would also be of interest, since one should expect obstructions when attempting to supersymmetrize this theory for a choice of parameters leaving only even Z 2 -parity corrections. Generalized Scherk-Schwarz reductions like those considered in [47,48] would also be interesting to examine in order to find higher-derivative corrections in gauged supergravities and to clarify the relation between α ′ -corrections and non-geometry (see for example [49][50][51][52][53][54][55] and references therein). Due to the field redefinitions involved in this construction, we expect the duality covariant scalars of the reduced theory to be related to the diffeomorphism and Lorentz covariant scalars through O(α ′ ) redefinitions that are quadratic in gaugings.…”

Doubled α ′-geometry

“…Double field theory formulations where the strong constraint is somewhat relaxed have been given for massive IIA supergravity in [29], for flux compactifications in [37,38], and explored in some generality in [39,40]. See also [41,42] for the geometric role of nongeometric fluxes in double field theory. Global aspects of double field theory are discussed in [22] where a formula for large gauge transformations was proposed and examined in detail.…”

Duality twisted reductions of Double Field Theory of Type II strings

“…Following this, in [26], it was shown that the weakening of the strong constraint in the twisted reductions of DFT implies that even non-geometric gaugings of half-maximal supergravity (meaning that they cannot be T-dualized to gauged supergravities arising from conventional compactifications of ten-dimensional supergravity) has an uplift to DFT. Such non-geometric gaugings also arise from compactifications of string theory with non-geometric flux (see, for example [27][28][29]) and the relation of such compactifications with twisted compactifications of DFT was explored in various papers, including [30][31][32][33]. We should also note that, the results of [22] was also obtained by [34], by considering the duality twisted reductions of the DFT action they constructed in terms of a torsionful, flat generalized connection, called the Weitzenböck connection.…”