Communications in Mathematical Physics

, Volume 337, Issue 2, pp 909–954 | Cite as

Spherical T-Duality

  • Peter Bouwknegt
  • Jarah Evslin
  • Varghese Mathai


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.


Spectral Sequence Cohomology Group Cohomology Class Chern Class Circle Bundle 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Peter Bouwknegt
    • 1
  • Jarah Evslin
    • 2
  • Varghese Mathai
    • 3
  1. 1.Department of Theoretical Physics, Research School of Physics and Engineering and Mathematical Sciences InstituteThe Australian National UniversityCanberraAustralia
  2. 2.High Energy Nuclear Physics Group, Institute of Modern PhysicsChinese Academy of SciencesLanzhouChina
  3. 3.Department of Pure MathematicsUniversity of AdelaideAdelaideAustralia

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