nLab
spherical T-duality

Contents

Context

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

String theory

Contents

Idea

Spherical T-duality (Bouwknegt-Evslin-Mathai 14a) is the name given to a variation of topological T-duality where the role of the circle S 1S^1, or the circle group U(1)U(1), is replaced by the 3-sphere S 3S^3, or the special unitary group SU(2)SU(2). Where topological T-duality relates pairs consisting of total spaces of U(1)U(1)-principal bundles equipped with a cocycle in degree-3 ordinary cohomology, spherical T-duality relates pairs consisting of SU(2)SU(2)-principal bundles (or just S 3S^3-fiber bundles (Bouwknegt-Evslin-Mathai 14b)) equipped with cocycles in degree-7 cohomology. As for topological T-duality, under suitable conditions spherical T-duality lifts to an isomorphism of twisted K-theory classes of these bundles with twisting by the 7-class.

In the approximation of rational super homotopy theory, topological spherical T-duality has been derived for the M5-brane, not on 11d super Minkowski spacetime itself, but on its M2-brane-extended super Minkowski spacetime, and from there on the exceptional super spacetime; see FSS 18a, reviewed in FSS 18b.

References

The idea is due to

which in the course considers higher Snaith spectra and higher order algebraic K-theory.

A special case of this general story is discussed in some detail in

The realization in M-theory at the level of rational super homotopy theory is derived in

Last revised on April 10, 2019 at 03:39:27. See the history of this page for a list of all contributions to it.