Abstract
The structure of a Standard Model family is derived in a class of brane models with a U(M)×U(N) factor, from two mildly anthropic requirements: a massless photon and a universe that does not turn into a plasma of massless charged particles. If we choose M=3 and N=2, the only option is shown to be the Standard Model with an undetermined number of families. We do not assume the U(1) embedding, charge quantization, family repetition, nor the fermion representations; all of these features are derived, assuming a doublet Higgs. With a slightly stronger assumption even the Higgs representation is determined. We also consider a more general class, requiring an asymptotically free strong SU(M) (with M⩾3) interaction from the first factor and an electromagnetic U(1) embedded in both factors. We allow Higgs symmetry breaking of the U(N)×U(1) flavor group by at most one Higgs boson in any representation, combined with any allowed chiral symmetry breaking by SU(M). For M=3 there is a large number of solutions with an unbroken U(1). In all of these, “quarks” have third-integral charges and color singlets have integer charges in comparison to leptons. Hence Standard Model charge quantization holds for any N. Only for N=2 these models allow an SU(5) GUT extension, but this extension offers no advantages whatsoever for understanding the Standard Model; it only causes complications, such as the doublet–triplet splitting problem. Although all these models have a massless photon, all except the Standard Model are ruled out by the second anthropic requirement. In this class of brane models the Standard Model is realized as a GUT with its intestines removed, to keep only the good parts: a GUT without guts.
Highlights
Susy-GUTs are the pinnacle of the symmetry-based approach to particle physics, which has brought us the phenomenal success of the Standard Model
We present it as a path towards a derivation of the Standard Model, because it almost looks as if it comes out inescapably from some simple algebra, just by requiring complexity to emerge from the simplest ingredients
We first focus on a class of gauge theories with a gauge group SU(3) × SU(2) × U (1) and a Higgs mechanism, and we demonstrate that in this class the Standard Model fermion representations and U (1) choice is the only solution to our conditions
Summary
Susy-GUTs are the pinnacle of the symmetry-based approach to particle physics, which has brought us the phenomenal success of the Standard Model. In [7] it was shown that a single Standard Model family is the minimal choice that is anomaly free, chiral and allows Higgs couplings, but it is clear from the start that field theory allows an infinity of non-minimal solutions. It was pointed out in [10,13] that the argument is invalidated if right-handed SU(3) × SU(2) singlets with arbitrary hypercharge are taken into account. We were pleasantly surprised to discover that it can be understood, but that in addition by considering alternatives we were able to appreciate its remarkable structure far better than ever
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