## Exceptional Jordan Strings/Membranes and Octonionic Gravity/p-branes

**Authors:** Carlos Castro

Nonassociative Octonionic Ternary Gauge Field Theories are revisited
paving the path to an analysis of the many physical applications of Exceptional
Jordan Strings/Membranes and Octonionic Gravity. The old
octonionic gravity constructions based on the split octonion algebra Os
(which strictly speaking is not a division algebra) is extended to the full
fledged octonion division algebra O. A real-valued analog of the
Einstein-Hilbert Lagrangian L = R involving sums of all the possible contractions
of the Ricci tensors plus their octonionic-complex conjugates is presented.
A discussion follows of how to extract the Standard Model group (the
gauge fields) from the internal part of the octonionic gravitational connection.
The role of Exceptional Jordan algebras, their automorphism
and reduced structure groups which play the roles of the rotation and
Lorentz groups is also re-examined. Finally, we construct (to our knowledge)
generalized novel octonionic string and p-brane actions and raise
the possibility that our generalized 3-brane action (based on a quartic
product) in octonionic flat backgrounds of 7, 8 octonionic dimensions may
display an underlying E7,E8 symmetry, respectively. We conclude with
some final remarks pertaining to the developments related to Jordan exceptional
algebras, octonions, black-holes in string theory and quantum
information theory.

**Comments:** 26 pages, submitted to the Journal of Physics A : Math and Theor

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### Submission history

[v1] 16 Mar 2011

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