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In physics, the Pati–Salam model is a Grand Unification Theory (GUT) proposed in 1974 by nobel laureate Abdus Salam and Jogesh Pati. The unification is based on there being four quark color charges, dubbed red, green, blue and violet (or lilac), instead of the conventional three, with the new "violet" quark being identified with the leptons. The model also has Left–right symmetry and predicts the existence of a high energy right handed weak interaction with heavy W' and Z' bosons.
Originally the fourth color was labelled "lilac" to alliterate with "lepton". Pati-Salam is a mainstream theory and a viable alternative to the Georgi–Glashow SU(5) unification. It can be embedded within an SO(10) unification model (as can SU(5)).
Core theory 
The Pati–Salam model states that the gauge group is either SU(4) × SU(2)L× SU(2)R or ( SU(4) × SU(2)L× SU(2)R ) / Z2 and the fermions form three families, each consisting of the representations (4,2,1) and . This needs some explanation. The center of SU(4)× SU(2)L× SU(2)R is Z4× Z2L× Z2R. The Z2 in the quotient refers to the two element subgroup generated by the element of the center corresponding to the 2 element of Z4 and the 1 elements of Z2L and Z2R. This includes the right-handed neutrino, which is now likely believed to exist. See neutrino oscillations. There is also a (4,1,2) and/or a scalar field called the Higgs field which acquires a VEV. This results in a spontaneous symmetry breaking from to or from to and also,
- (q and l),
- (dc, uc, ec and νc),
, and . See restricted representation. Of course, calling the representations things like and (6,1,1) is purely a physicist's convention, not a mathematician's convention, where representations are either labelled by Young tableaux or Dynkin diagrams with numbers on their vertices, but still, it is standard among GUT theorists.
The weak hypercharge, Y, is the sum of of SU(4) and of SU(2)R
Actually, it is possible to extend the Pati-Salam group so that it has two connected components. The relevant group is now the semidirect product . The last Z2 also needs explaining. It corresponds to an automorphism of the (unextended) Pati-Salam group which is the composition of an involutive outer automorphism of SU(4) which isn't an inner automorphism with interchanging the left and right copies of SU(2). This explains the name left and right and is one of the main motivations for originally studying this model. This extra "left-right symmetry" restores the concept of parity which had been shown not to hold at low energy scales for the weak interaction. In this extended model, is an irrep and so is . This is the simplest extension of the minimal left-right model unifying QCD with B−L.
This model doesn't predict gauge mediated proton decay (unless it is embedded within an even larger GUT group).
Differences from the SU(5) unification 
As mentioned above, both the Pati-Salam and Georgi–Glashow SU(5) unification models can be embedded in a SO(10) unification. The difference between the two models then lies in the way that the SO(10) symmetry is broken, generating different particles that may or may not be important at low scales and accessible by current experiments. If we look at the individual models, the most important difference is in the origin of the weak hypercharge. In the SU(5) model by itself there is no left-right symmetry (although there could be one in a larger unification in which the model is embedded), and the weak hypercharge is treated separately from the color charge. In the Pati–Salam model, part of the weak hypercharge (often called U(1)B-L) starts being unified with the color charge in the SU(4)C group, while the other part of the weak hypercharge is in the SU(2)R. When those two groups break then the two parts together eventually unify into the usual weak hypercharge U(1)Y.
Minimal supersymmetric Pati-Salam 
The N=1 superspace extension of 3+1 Minkowski spacetime
Spatial symmetry 
N=1 SUSY over 3+1 Minkowski spacetime with R-symmetry
Gauge symmetry group 
[SU(4)× SU(2)L × SU(2)R]/Z2
Global internal symmetry 
Vector superfields 
Those associated with the SU(4)× SU(2)L × SU(2)R gauge symmetry
Chiral superfields 
As complex representations:
label description multiplicity SU(4)×SU(2)L× SU(2)R rep R A GUT Higgs field 1 0 0 GUT Higgs field 1 0 0 singlet 1 2 0 electroweak Higgs field 1 0 0 no name 1 2 0 matter field 3 1 1 matter field 3 1 -1 sterile neutrino 3 1 1
A generic invariant renormalizable superpotential is a (complex) and U(1)R invariant cubic polynomial in the superfields. It is a linear combination of the following terms:
and are the generation indices.
Left-right extension 
We can extend this model to include left-right symmetry. For that, we need the additional chiral multiplets and
- Graham G. Ross, Grand Unified Theories, Benjamin/Cummings, 1985, ISBN 0-8053-6968-6
- Anthony Zee, Quantum Field Theory in a Nutshell, Princeton U. Press, Princeton, 2003, ISBN 0-691-01019-6
- J. Pati and A. Salam, Phys. Rev. D10 (1974), 275. Lepton number as the fourth "color"
- J.C. Baez, J. Huerta (2009). "The Algebra of Grand Unified Theories". arXiv:0904.1556 [hep-th].
- Pati-Salam model on Scholarpedia
- Proton decay, annihilation or fusion? by Wu, Dan-Di; Li, Tie-Zhong, Zeitschrift für Physik C, Volume 27, Issue 2, pp. 321–323 preview Fusion of all three quarks is the only decay mechanism mediated by the Higgs particle, not the gauge bosons, in the Pati-Salam model
- The Algebra of Grand Unified Theories John Huerta. Slide show: contains an overview of Pati-Salam
- the Pati-Salam model Motivation for the Pati–Salam model