Timelike Hopf duality and type IIA * string solutions

DOI10.1088/0264-9381/17/3/305zbMATH Open1156.81451arXivhep-th/9905161OpenAlexW3103302262MaRDI QIDQ4946992

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Publication date: 23 March 2000

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Abstract: The usual T-duality that relates the type IIA and IIB theories compactified on circles of inversely-related radii does not operate if the dimensional reduction is performed on the time direction rather than a spatial one. This observation led to the recent proposal that there might exist two further ten-dimensional theories, namely type IIA^* and type IIB^*, related to type IIB and type IIA respectively by a timelike dimensional reduction. In this paper we explore such dimensional reductions in cases where time is the coordinate of a non-trivial U(1) fibre bundle. We focus in particular on situations where there is an odd-dimensional anti-de Sitter spacetime AdS_{2n+1}, which can be described as a U(1) bundle over widetilde{CP}^n, a non-compact version of CP^n corresponding to the coset manifold SU(n,1)/U(n). In particular, we study the AdS_5 imes S^5 and AdS_7 imes S^4 solutions of type IIB supergravity and eleven-dimensional supergravity. Applying a timelike Hopf T-duality transformation to the former provides a new solution of the type IIA^* theory, of the form widetilde{CP}^2 imes S^1 imes S^5. We show how the Hopf-reduced solutions provide further examples of ``supersymmetry without supersymmetry. We also present a detailed discussion of the geometrical structure of the Hopf-fibred metric on AdS_{2n+1}, and its relation to the horospherical metric that arises in the AdS/CFT correspondence.

Full work available at URL: https://arxiv.org/abs/hep-th/9905161

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