Fermion Content
Chiral anomaly:
Triangle diagram ∝ Tr[T_a{T_b,T_c}] where T are gauge generators.
SM cancellation:
For each generation: quarks (3 colors) + leptons. Sum: [U³] − [D³] + [L³] − [N³] = 0 exactly!
Conditions:
• [Y³]: Σ Y³ = 0
• [Y]: Σ Y = 0
• [SU(2)²Y]: Σ_{doublets} Y = 0
• [SU(3)²Y]: Σ_{quarks} Y = 0
Green-Schwarz:
In string theory, anomalies can cancel via B-field shift.
Triangle diagram ∝ Tr[T_a{T_b,T_c}] where T are gauge generators.
SM cancellation:
For each generation: quarks (3 colors) + leptons. Sum: [U³] − [D³] + [L³] − [N³] = 0 exactly!
Conditions:
• [Y³]: Σ Y³ = 0
• [Y]: Σ Y = 0
• [SU(2)²Y]: Σ_{doublets} Y = 0
• [SU(3)²Y]: Σ_{quarks} Y = 0
Green-Schwarz:
In string theory, anomalies can cancel via B-field shift.