Duality orbits of non‐geometric fluxes

Abstract

Key words Double field theory, gauged supergravities, flux compactifications.Compactifications in duality covariant constructions such as generalised geometry and double field theory have proven to be suitable frameworks to reproduce gauged supergravities containing non-geometric fluxes. However, it is a priori unclear whether these approaches only provide a reformulation of old results, or also contain new physics. To address this question, we classify the T-and U-duality orbits of gaugings of (half-)maximal supergravities in dimensions seven and higher. It turns out that all orbits have a geometric supergravity origin in the maximal case, while there are non-geometric orbits in the half-maximal case. We show how the latter are obtained from compactifications of double field theory.

Extended geometry and gauged maximal supergravity

“…So, while the relaxed constraints are necessary and sufficient for gauge consistency in this case, the section condition is only sufficient. In DFT, explicit examples of truly extended configurations were found in [56], and it would be interesting to find some here as well.…”

“…When relaxed, the connection between this construction and higher dimensional supergravity is less clear and should be understood better. Configurations that satisfy the relaxed constraints but not the section condition lie beyond supergravity compactifications, and are therefore strictly non-geometric (we refer to [56] for a discussion on these issues). Whether they correspond to allowed configurations in the full string or M-theory is a question that remains partially unanswered and worth exploring.…”

“…It is known that the section condition implies that this framework is a covariant re-writing of higher-dimensional supergravity compactifications. In this kind of compactifications only a subset of the gaugings can be reached in the lower dimensional effective action, and thus the space of gauging orbits is split into those that can be obtained (geometric) and those that cannot (non-geometric) [56]. Restricting to Scherk-Schwarz-type backgrounds, this construction does not necessarily use the section condition, and instead uses the twisted conditions, which are in one to one correspondence with the constraints of gauged supergravity.…”

On the exceptional generalised Lie derivative for d ≥ 7

“…This implies that they depend on only ten coordinates and, therefore, locally DFT is equivalent to generalised geometry. The strong constraint can be locally relaxed [12][13][14]. Some works in the direction of understanding, from the world sheet perspective, the origin of the strong constraint and its possible relaxation have appeared in the literature [15][16][17].…”

Matrix theory origins of non-geometric fluxes

“…More recently, a ten-dimensional description of non-geometric fluxes was investigated in the context of generalized geometry [38,39], double field theory [40][41][42][43] and non-associative geometry [44,45] …”