Schreiber The Hidden M-Group

An article that we are finalizing at CQTS:

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• Grigorios Giotopoulos, $\;$ Hisham Sati $\;$ and $\,$ Urs Schreiber:

  
  

  The Hidden M-Group

  
  

  download:

  • manuscript pdf to appear here

  • teaser: pdf

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Abstract. The basic M-algebra, namely 11d susy extended by M-brane central charges, famously admits a “hidden” fermionic extension which supports a richly structured super-invariant avatar of the M-theory 3-form, which becomes closed in a limit in which local Lorentz-symmetry enhances to $\mathrm{Sp}(32)$ (in fact further to $\mathrm{CSp}(32)$).

Here we understand this symmetry-enhanced hidden M-algebra as the super-space version of an exceptional generalized tangent space model for fully reduced 11d supergravity, and its closed 3-form as the M-theoretic lift of the Poincaré 2-form (that controls T-duality on doubled spacetime).

Therefore we look to promote it to a Kleinian model space for super-exceptional Cartan geometry, hence to an actual super-Lie group: the hidden M-group extending 11d spacetime by manifesting both its super- as well as much of its U-duality symmetry. Actual sections (only alluded to by the “section conditions” of exceptional field theory) of this super-Lie extension encode M-theory super 3-form field configurations in super-exceptional coordinates, for which we give explicit formulas.

To deal with subtleties in the construction we also (1.) provide a computer-checked re-derivation of the hidden M-algebra and of its super-invariant 3-form, and we (2.) present a streamlined conception of super-Lie groups and their super-Lie integration which is both rigorous while still close to physics practice.

Followup to:

• Super-exceptional embedding construction of the M5-brane

• Super-exceptional M5-brane model – Emergence of SU(2)-flavor sector