Spherical T-Duality

We introduce spherical T-duality, which relates pairs of the form (P, H) consisting of a principal SU(2)-bundle (Formula presented.) and a 7-cocycle H on P. Intuitively spherical T-duality exchanges H with the second Chern class c₂(P). Unless (Formula presented.), 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 (Formula presented.), also their integral twisted cohomologies and, when (Formula presented.), 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.