Abstract
We investigate the lifting of half-maximal four-dimensional gauged supergravities to compactifications of string theory. It is shown that a class of such supergravities can arise from compactifications of IIA string theory on manifolds of SU(2)-structure which may be thought of as K3 fibrations over T^2. Examples of these SU(2)-structure backgrounds, as smooth K3 bundles and as compactifications with H-flux, are given and we also find evidence for a class of non-geometric, Mirror-fold backgrounds. By applying the duality between IIA string theory on K3 and Heterotic string theory on T^4 fibrewise, we argue that these SU(2)-structure backgrounds are dual to Heterotic compactifications on a class T^4 fibrations over T^2. Examples of these fibrations as twisted tori, H-flux and T-fold compactifications are given. We also construct a new set of backgrounds, particular to Heterotic string theory, which includes a previously unknown class of Heterotic T-folds. A sigma model description of these backgrounds, from the Heterotic perspective, is presented in which we generalize the Bosonic doubled formalism to Heterotic string theory.
Highlights
The study of gauged supergravities has received a new impetus in recent years
One may argue from very general topological considerations, that a reduction on a manifold of reduced structure group explicitly breaks some supersymmetry [1, 2, 3, 4]
We will only consider reductions of IIA and Heterotic string theory on SU (2)- and 1I-structure backgrounds respectively here and we shall be interested in realizing these reductions as compactifications on internal spaces which we shall identify
Summary
The study of gauged supergravities has received a new impetus in recent years. This has been due, in part, to the application of novel techniques and concepts, such as generalized geometry, in constructing and analyzing new dimensional reduction scenarios. One might say that many of the N = 1 and N = 2 gauged supergravities mentioned above are well understood at the level of a dimensional reduction - an algorithm to construct one supergravity from another, higher-dimensional, supergravity - but are yet to be fully understood as compactifications in the rigorous Kaluza-Klein sense It is, quite difficult to construct explicit examples of SU (n)-structure manifolds of 2n real dimensions. There is mounting evidence that many gauged supergravities can not arise from a compactification of a higher dimensional supergravity on a conventional manifold, but can be lifted to string theory on a non-geometric background Such backgrounds have no analogue in field theories such as General Relativity and shed light on possible stringor M-theoretic generalizations of spacetime [10, 11, 12].
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