Grand unfication models from \(SO(32)\) heterotic stringAt least in the 1980s, the \(E_8\times E_8\) heterotic string theory was the main phenomenologically relevant class of string compactifications, the main candidate for a theory of everything. However, there's another possible gauge group of heterotic strings in \(D=10\), namely \(SO(32)\), more precisely \(Spin(32)/\ZZ_2\).

This has been considered phenomenologically dead by many because the group isn't a nice grand unified group. Also, this heterotic string theory has a spinor matter. But the chiral spinors of \(Spin(32)\) form a huge, 32768-dimensional representation. On top of that, all these spinor states are massive (string-mass-scale masses). Note that this heterotic string theory is S-dual to type I string theory and these massive spinor states are stable and arise as excitations of a non-supersymmetric D0-brane in the type I theory, an insight of the mid 1990s.

There have been some semi-realistic constructions starting with \(SO(32)\) heterotic string theory. However, this Kim's paper is the first group of models that does lead to GUT as an intermediate points, with the help of some \(\ZZ_{12-I}\) orbifolds. The \(SU(9)\) which has been known to be possible for "family GUT" is embedded "maximally" into \(SU(16)\) inside \(SO(32)\). See the paper for the rest. More detailed explanations are a waste of time to write for the general public whose overwhelming majority is only capable of reading crackpots' diatribes against string theory, quantum mechanics, against mathematics as well as aesthetic considerations in physics, and similar utter garbage.

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