ON OCTONIONIC GRAVITY, EXCEPTIONAL JORDAN STRINGS AND NONASSOCIATIVE TERNARY GAUGE FIELD THEORIES

摘要

Novel nonassociative octonionic ternary gauge field theories are proposed based on anternary bracket. This paves the way to the many physical applications of exceptionalnJordan Strings/Membranes and Octonionic Gravity. The old octonionic gravity constructionsnbased on the split octonion algebra Os (which strictly speaking is not a divisionnalgebra) is extended to the full fledged octonion division algebra O. A real-valued analognof the Einstein–Hilbert Lagrangian L = R involving sums of all the possible contractionsnof the Ricci tensors plus their octonionic-complex conjugates is presented. A discussionnfollows of how to extract the Standard Model group (the gauge fields) from the internalnpart of the octonionic gravitational connection. The role of exceptional Jordan algebras,ntheir automorphism and reduced structure groups which play the roles of the rotationnand Lorentz groups is also re-examined. Finally, we construct (to our knowledge) generalizednnovel octonionic string and p-brane actions and raise the possibility that ourngeneralized 3-brane action (based on a quartic product) in octonionic flat backgroundsnof 7, 8 octonionic dimensions may display an underlying E7,E8 symmetry, respectively.nWe conclude with some final remarks pertaining to the developments related to Jordannexceptional algebras, octonions, black-holes in string theory and quantum informationntheory