Spherical T-Duality |
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| Authors: | Peter Bouwknegt Jarah Evslin Varghese Mathai |
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| Affiliation: | 1.Department of Theoretical Physics, Research School of Physics and Engineering and Mathematical Sciences Institute,The Australian National University,Canberra,Australia;2.High Energy Nuclear Physics Group, Institute of Modern Physics,Chinese Academy of Sciences,Lanzhou,China;3.Department of Pure Mathematics,University of Adelaide,Adelaide,Australia |
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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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