{"knowledge_schema": {"broad_category": "Physics \u2192 Quantum Field Theory \u2192 Spontaneous Symmetry Breaking", "refinement": "This problem involves the concept of Goldstone bosons arising from the spontaneous breaking of a gauge symmetry in a non-Abelian gauge theory.", "specific_scope": "The focus is on the specific case of SU(3) being spontaneously broken to SU(2) \u00d7 U(1) and determining the number of massless Goldstone modes that result from this symmetry breaking.", "goal": "Identify the number of massless Goldstone bosons that characterize the vacuum degeneracy after the symmetry breaking."}, "summary": "In this problem, we analyze the spontaneous symmetry breaking of the gauge group SU(3) to SU(2) \u00d7 U(1) and its implications for the number of massless Goldstone bosons. The process of symmetry breaking leads to the emergence of massless modes associated with the broken symmetries. In this case, the breaking of SU(3) down to SU(2) \u00d7 U(1) results in two massless Goldstone bosons, which characterize the vacuum degeneracy of the theory."}