Spherical T-duality

Abstract

We introduce spherical T-duality, which relates pairs of the form (P, H) consisting of a principal SU(2)-bundle P→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)≤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)≤7, also their integral twisted cohomologies and, when dim(M)≤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.