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

References in corpus (4)

• On the Topology and Flux of T-Dual Manifolds
• T-duality for principal torus bundles
• What Does(n't) K-theory Classify?
• A Higher Twist in String Theory

Cited by in corpus (1)

• Spherical T-duality II: An infinity of spherical T-duals for non-principal SU(2)-bundles