Schreiber Super-Lie-infinity T-Duality and M-Theory

An article that we are finalizing at CQTS:



on super-space T-duality and its potential lifts to M-theory.

Abstract. Super L L_\infty -algebras unify extended super-symmetry with rational classifying spaces for higher flux densities: The super-invariant super-fluxes which control super p p -branes and their supergravity target super-spaces are, together with their (non-linear) Bianchi identities, neatly encoded in (non-abelian) super- L L_\infty cocycles, these being the rational shadows of flux-quantization laws (in ordinary cohomology, K-theory, Cohomotopy, iterated K-theory, …).

We first review, in streamlined form and filling some previous gaps, double-dimensional reduction/oxidation and 10D superspace T-duality along higher-dimensional super-tori, tangent super-space wise as an instance of adjunctions (dualities) between super- L L_\infty -extensions and -cyclifications, thereby deriving the proposed laws of “topological T-duality”, at the rational level, from the super- L L_\infty structure of type II super-space.

Then, by considering super-space T-duality along all 1+9 spacetime dimensions while retaining the 11th dimension as in F-theory, we find the M-algebra appear as the D/NS5-brane extension of the fully T-doubled/correspondence super-spacetime. On this backdrop we recognize the “decomposed” M-theory 3-form on the “hidden M-algebra” as an M-theoretic lift of the Poincaré super 2-form that controls superspace T-duality (as the integral kernel of the super Fourier-Mukai transform).

Recalling that the hidden M-algebra appears also in a higher form of rational-topological T-duality where strings are replaced by M5-branes, we end with comments on the M-algebra as a Kleinian local model space for U-duality-covariant superspace supergravity.


Following up on:

Fiorenza, Sati, Schreiber:


Last revised on October 30, 2024 at 15:52:21. See the history of this page for a list of all contributions to it.