Schreiber Super T-Duality inside the Superpoint

A talk that I will have given:

Abstract. Twisted cohomology is maps in the tangent homotopy theory or parameterized spectra1. There is a Quillen-Sullivan-type model for its rationalization via unbounded L-∞ algebras2. Examples appear by iterated maximal higher central extensions of super L-∞ algebras which are invariant with respect to all automorphisms modulo R-symmetries – a super-equivariant version of the Whitehead tower. Applied to the superpoint, this process discovers all the twisted cohomology seen in string/M-theory3\,4, rationally, in particular twisted topological K-theory with 5-brane correction and with supersymmetric Chern-forms on 10d-superspace5. This comes out of the M-brane coefficients, which turn out to be the 4-sphere6, via these rational equivalences \,:

S 4/S 1,6ku/BU(1)andΣ S 3 (S 4/S 1)ku/BU(1). \mathcal{L}S^4/S^1 \underset{\mathbb{Q}, \leq 6}{\simeq} ku/BU(1) \;\;\; \text{and} \;\;\; \Sigma^\infty_{S^3} (S^4/S^1) \underset{\mathbb{Q}}{\simeq} ku/BU(1) \oplus \cdots \,.

Passage to cyclic? L-∞ cohomology reflects double dimensional reduction of super p-branes. Applied to twisted K-theory this yields a super L-∞ isomorphism exhibiting supersymmetric topological T-duality, rationally7. The super L-∞ algebra it classifies is the local tangent complex of super T-folds.

These rational phenomena indicate that integrally the super-equivariant Whitehead tower should discover extremely interesting twisted super-differential cohomology theories. Possibly one should promote super L-∞ algebras to spectral super-schemes, namely spectral schemes over an even periodic ring spectrum, and then repeat the process.

Lecture notes with more details are here:

  • geometry of physics – fundamental super p-branes?.

Last revised on March 3, 2017 at 04:45:12. See the history of this page for a list of all contributions to it.