Consistency of the \(\text{AdS}_7\times S_4\) reduction and the origin of self-duality in odd dimensions
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Publication:5934913
DOI10.1016/S0550-3213(00)00193-0zbMATH Open0985.83026arXivhep-th/9911238OpenAlexW2064170844WikidataQ60145278 ScholiaQ60145278MaRDI QIDQ5934913
Author name not available (Why is that?)
Publication date: 14 May 2001
Published in: (Search for Journal in Brave)
Abstract: We discuss the full nonlinear Kaluza-Klein (KK) reduction of the original formulation of d=11 supergravity on to gauged maximal ({cal N}=4) supergravity in 7 dimensions. We derive the full nonlinear embedding of the d=7 fields in the d=11 fields (``the ansatz) and check the consistency of the ansatz by deriving the d=7 supersymmetry laws from the d=11 transformation laws in the various sectors. The ansatz itself is nonpolynomial but the final d=7 results are polynomial. The correct d=7 scalar potential is obtained. For most of our results the explicit form of the matrix U connecting the d=7 gravitino to the Killing spinor is not needed, but we derive the equation which U has to satisfy and present a solution. Requiring that the expression in d=11 can be written as , we find the ansatz for the 4-form F. It satisfies the Bianchi identities. The corresponding ansatz for A modifies the geometrical proposal by Freed et al. by including d=7 scalar fields. A first order formulation for the three index photon in d=11 is needed to obtain the d=7 supersymmetry laws and the action for the nonabelian selfdual antisymmetric tensor field . Therefore selfduality in odd dimensions originates from a first order formalism in higher dimensions.
Full work available at URL: https://arxiv.org/abs/hep-th/9911238
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