Chiral scalar fields, custodial symmetry in electroweak SU(2)L × U(1) and the quantization of the electric charge

I study the scalar representations of the electroweak group of the Standard Model, which is a subgroup of the chiral group U(N)l × U(N)r with N flavours, for N even, with a special emphasis on their chiral properties and on their behaviour by the discrete symmetries P and CP. They exhaust the 2N2 scalar and pseudoscalar degrees of freedom of the chiral group, for which a SU(2)l × U(1) renormalizable, anomaly-free gauge theory naturally springs out. It is shown to have a global diagonal SU(2)v symmetry independently of the value of the hypercharge coupling, which becomes local at the limit when the latter vanishes. When acting in the 4-dimensional space of states spanned by the special representations under scrutiny in this paper, the electric charge is one of the three generators of this “custodial” symmetry; that the latter stays an unbroken symmetry is thus correlated with the quantization of the electric charge.