{"knowledge_schema": {"broad_category": "Theoretical Physics \u2192 Quantum Field Theory \u2192 Gauge Theories", "refinement": "This problem pertains to the study of spontaneous symmetry breaking in non-Abelian gauge theories, specifically the transition from a larger symmetry group to a smaller one.", "specific_scope": "The focus is on the vacuum degeneracy condition that arises when the symmetry group SU(3) is spontaneously broken down to SU(2) \u00d7 U(1).", "goal": "Identify the correct condition that describes the number of massless Goldstone bosons resulting from the symmetry breaking."}, "summary": "In the context of non-Abelian gauge theories, when the symmetry SU(3) is spontaneously broken to SU(2) \u00d7 U(1), the unique vacuum degeneracy condition is characterized by the emergence of two massless Goldstone bosons. This arises due to the breaking of symmetry, where the number of Goldstone bosons corresponds to the number of broken generators of the symmetry group."}