An Introduction To Quantum Field Theory - M. Peskin, D. Schroeder (Perseus, 1995) · Problem 20.1

Electroweak Theory: Basics — M. Peskin, D. Schroeder (Perseus, 1995)

Physics — QFT · spontaneous-symmetry-breaking-su5

Problem

Consider a gauge theory with the gauge group SU(5)SU(5), coupled to a scalar field Φ\Phi in the adjoint representation. Assume that the potential for this scalar field forces it to acquire a nonzero vacuum expectation value. Two possible choices for this expectation value are ⟨Φ⟩=A(1111−4)and⟨Φ⟩=B(222−3−3).\langle\Phi\rangle = A \begin{pmatrix} 1 & & & & \\ & 1 & & & \\ & & 1 & & \\ & & & 1 & \\ & & & & -4 \end{pmatrix} \quad \text{and} \quad \langle\Phi\rangle = B \begin{pmatrix} 2 & & & & \\ & 2 & & & \\ & & 2 & & \\ & & & -3 & \\ & & & & -3 \end{pmatrix}. For each case, work out the spectrum of gauge bosons and the unbroken symmetry group.

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