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Spherical T-Duality

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Abstract

We introduce spherical T-duality, which relates pairs of the form (P, H) consisting of a principal SU(2)-bundle \({P \rightarrow M}\) and a 7-cocycle H on P. Intuitively spherical T-duality exchanges H with the second Chern class c 2(P). Unless \({dim(M) \leq 4}\), not all pairs admit spherical T-duals and the spherical T-duals are not always unique. Nonetheless, we prove that all spherical T-dualities induce a degree-shifting isomorphism on the 7-twisted cohomologies of the bundles and, when \({dim(M) \leq 7}\), also their integral twisted cohomologies and, when \({dim(M) \leq 4}\), even their 7-twisted K-theories. While spherical T-duality does not appear to relate equivalent string theories, it does provide an identification between conserved charges in certain distinct IIB supergravity and string compactifications.

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Authors and Affiliations

  1. Department of Theoretical Physics, Research School of Physics and Engineering and Mathematical Sciences Institute, The Australian National University, Canberra, ACT, 2601, Australia

    Peter Bouwknegt

  2. High Energy Nuclear Physics Group, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, China

    Jarah Evslin

  3. Department of Pure Mathematics, University of Adelaide, Adelaide, SA, 5005, Australia

    Varghese Mathai

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  1. Peter Bouwknegt
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  2. Jarah Evslin
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  3. Varghese Mathai
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Correspondence to Varghese Mathai.

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Communicated by H. Ooguri

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Bouwknegt, P., Evslin, J. & Mathai, V. Spherical T-Duality. Commun. Math. Phys. 337, 909–954 (2015). https://doi.org/10.1007/s00220-015-2354-4

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