Spherical T-Duality

Abstract

We introduce spherical T-duality, which relates pairs of the form $(P,H)$ consisting of a principal $SU(2)$-bundle $P\to M$ and a 7-cocycle $H$ on $P$. Intuitively spherical T-duality exchanges $H$ with the second Chern class $c_2(P)$. Unless $dim(M)\le 4$, 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 $dim(M)\le 7$, also their integral twisted cohomologies and, when $dim(M)\le 4$, 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.

45 pages, clarification on the definition of 7-cocycle twisted K-theory included in Section 6.1.2

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Cited by in corpus (8)

• Higher T-duality in M-theory via local supersymmetry
• Spherical T-duality II: An infinity of spherical T-duals for non-principal SU(2)-bundles
• Twisted iterated algebraic K-theory and topological T-duality for sphere bundles
• Spherical T-Duality and the spherical Fourier-Mukai transform
• Topological T-duality via Lie algebroids and $Q$-flux in Poisson-generalized geometry
• On the Chern character in Higher Twisted K-theory and spherical T-duality
• Computations in higher twisted $K$-theory
• Geometry of Membrane Sigma Models