An Introduction to non-geometric backgrounds in string theory.

Abstract: There has been much progress recently in giving a string theory origin to many gauged supergravities. In particular, a considerable number of gauged supergravities may be understood as arising from a compactification on a conventional manifold; however, there is evidence that many gauged supergravities arise from string theory on a non-geometric background. Examples of non-geometric backgrounds include T-Folds, where the background is patched together by symmetries which may include T-dualities. Such backgrounds do not admit a description in terms of Riemannian geometry and provide a characteristic signature of stringy physics. In these introductory lectures I shall introduce a series of non-geometric backgrounds from both the target space and worldsheet perspective and discuss connections with the duality symmetries of string theory. The focus will be on backgrounds arising from maximal supergravities but, time permitting, I will also discuss supergravities with less supersymmetry.