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Title: 'Solution to the RCHO single-copy problem'
Abstract: Peering in from the outside, RCHO looks to be an ideal mathematical structure for particle physics. It is 32C dimensional - exactly the size of a generation of fermions, including a RH neutrino. Its left- and right-multiplication algebras generate the Clifford algebra Cl(10), and so one has automatic access to Spin(10) symmetry, (and consequently those symmetries for Pati-Salam, Georgi-Glashow, the LR symmetric model, and the standard model). Furthermore, it contains extra algebraic structure beyond Cl(10), which is seen to break Spin(10) to Pati-Salam symmetries, and SU(5) to the standard model symmetries.
However, this line of research has been weighted down by a difficulty known as the single-copy problem. That is, a satisfactory description of spin has so far only been achieved by taking two copies of the algebra, instead of one. Arguably, this doubling of states ruins much of RCHO’s original appeal.
In this talk, we describe how we have solved the single-copy problem. We then explain three developments which ensued:
(1) We demonstrate how a cascade of complex structures connect
Spin(10), Pati-Salam, the LR symmetric model, the standard model, and
the standard model’s unbroken gauge symmetries.
(2) We demonstrate how our model treats internal gauge and local
spacetime symmetries in fundamentally different, yet complementary,
ways.
(3) We demonstrate a novel Higgs sector resulting from a phenomenon
known as quaternionic triality.
This is joint work together with Dr Mia Hughes.