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SUMMARY:Jordan algebras: from QM to 5D supergravity to … Standard Model?
DTSTART;VALUE=DATE-TIME:20210503T160000Z
DTEND;VALUE=DATE-TIME:20210503T170000Z
DTSTAMP;VALUE=DATE-TIME:20220518T223530Z
UID:indico-contribution-84@events.perimeterinstitute.ca
DESCRIPTION:Speakers: Paul Townsend (University of Cambridge)\nThis talk w
ill be about two applications of Jordan algebras. The first\, to quantum m
echanics\, follows on from the talk of John Baez. I will explain how time
dependence makes use of the associator\, and how this is related to the co
mmutator in the standard density matrix formulation.\n\nThe associator of
a Jordan algebra also determines the curvature of a Riemannian metric on i
ts positive cone\, invariant under the symmetry group of the norm (mention
ed in the talk of John Baez)\; the cone is foliated by hypersurfaces of co
nstant norm. This geometry is relevant to a class of N=2 5D supergravity t
heories (from the early 1980s) which arise (in some cases\, at least) fro
m Calabi-Yau compactification of 11D supergravity. The 5D interactions ar
e determined by the structure constants of a euclidean Jordan algebra wit
h cubic norm. The exceptional JA of 3x3\noctonionic matrices yields an ``
exceptional’’ 5D supergravity which yields\, on reduction to 4D\, an
``exceptional’’ N=2 supergravity with many similarities to N=8 supergr
avity\, such as a non-compact global E7 symmetry. However\, it has a compa
ct `composite’ E6 gauge invariance (in contrast to the SU(8) of N=8 sup
ergravity). An old speculation is that non-perturbative effects break the
N=2 supersymmetry and cause the E6 gauge potentials to become the dynamica
l fields of an E6 GUT. Potentially (albeit improbably) this provides a con
nection between M-theory\, the exceptional Jordan algebra\, and the Standa
rd Model.\n\nhttps://events.perimeterinstitute.ca/event/5/contributions/84
/
LOCATION:
URL:https://events.perimeterinstitute.ca/event/5/contributions/84/
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