Left-right symmetry

In theoretical physics, the electroweak model breaks parity maximally. All its fermions are chiral Weyl fermions. Some theorists found this objectionable, and so proposed a GUT extension of the electroweak group

${[SU(2)_W\times U(1)_Y]\over \mathbb{Z}_2}$

${SU(2)_L\times SU(2)_R\times U(1)_{B-L}\over \mathbb{Z}_2}$ .

Here, SU(2)_L (pronounced SU(2) left) is none other than SU(2)_W and B-L is the baryon number minus the lepton number.

There is also the chromodynamic SU(3)_C. The idea was to restore parity by introducing a left-right symmetry. This is a group extension of Z₂ (the left-right symmetry) by

${SU(3)_C\times SU(2)_L \times SU(2)_R \times U(1)_{B-L}\over \mathbb{Z}_6}$

to the semidirect product

${SU(3)_C\times SU(2)_L \times SU(2)_R \times U(1)_{B-L}\over \mathbb{Z}_6}$ Missing image
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Z₂.

This has two connected components where Z₂ acts as an automorphism, which is the composition of an involutive outer automorphism of SU(3)_C with the interchange of the left and right copies of SU(2) with the reversal of U(1)_B-L. This left-right symmetry is spontaneously broken to give a chiral low energy theory.

In this setting the chiral quarks

(3,2,1)_1/3

and

$(\bar{3},1,2)_{-{1\over 3}}$

are unified into an irrep

$(3,2,1)_{1\over 3}\oplus(\bar{3},1,2)_{-{1\over 3}}$ .

The leptons are also unified into an irrep

$(1,2,1)_{-1}\oplus(1,1,2)_1$ .

This then predicts three sterile neutrinos, which is perfectly consistent with current neutrino oscillation data.

Because the left-right symmetry is spontaneously broken, left-right models predict domain walls.

Later, this left-right symmetry idea was used in the Pati-Salam model and trinification.

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Left-right symmetry

See also: Left-right symmetry, As of 2005, Automorphism, B-L, Baryon number, Chirality (physics), Chromodynamic, Connected component, Domain wall