 Such an SU(2)R symmetry can never be exact and unbroken because otherwise, the up-type and the down-type Yukawa couplings will be exactly identical.SU(2)R does not map the hypercharge symmetry U(1)Y to itself but the hypercharge gauge coupling strength is small and in the limit as it goes to zero, we won't have a problem.U(1)Y is said to be weakly gauged and this explicitly breaks SU(2)R.

After the Higgs doublet acquires a nonzero vacuum expectation value, the (approximate) SU(2)L × SU(2)R symmetry is spontaneously broken to the (approximate) diagonal subgroup SU(2)V. This approximate symmetry is called the custodial symmetry.