A. Zee, Quantum Field Theory in a Nutshell · Problem IV.6.1

Field Theory Redux

Physics — QFT

Problem

Consider an

SU(5)

gauge theory with a Higgs field

\phi

transforming as the 5-dimensional representation:

\phi^i, i = 1, 2, \ldots, 5

. Show that a vacuum expectation value of

\phi

breaks

SU(5)

SU(4)

. Now add another Higgs field

\phi'

, also transforming as the 5-dimensional representation. Show that the symmetry can remain at

SU(4)

or be broken to

SU(3)