 The classical potential is

This vanishes on the moduli space, so the vacuum expectation value of formula_4 can be gauge rotated into Cartan subalgebra, making it a traceless diagonal complex matrix formula_5.Because the fields formula_4 no longer have vanishing vacuum expectation value, other fields become heavy due to the Higgs effect.They are integrated out in order to find the effective formula_2 Abelian gauge theory.