Yang-Mills theory is the non-Abelian gauge theory with field strengthUnder an infinitesimal gauge transformation it transforms covariantly as .
In four dimensions the Yang-Mills theta term is proportional to . Its density is a total derivative, but nontrivial gauge-field topology can make its spacetime integral physically relevant in the quantum theory.
A quantum anomaly is the failure of a classical symmetry to survive quantization because the functional measure or regulator cannot preserve it.
A gauge anomaly destroys a gauge redundancy needed to remove unphysical states and makes the quantum gauge theory inconsistent unless the anomaly cancels.
The chiral anomaly is the quantum nonconservation of a classically conserved axial current in a gauge-field background.
For massless Dirac fermions, the classical axial current is . The chiral anomaly makes its divergence proportional to .
A 't Hooft anomaly is an obstruction to gauging a global symmetry. It is preserved by renormalization-group flow and constrains possible infrared phases.
't Hooft anomaly matching requires the massless infrared degrees of freedom, topological sector, or symmetry-breaking pattern to reproduce every anomaly of an unbroken global symmetry measured in the ultraviolet theory.
Articles by others on the same topic
Yang–Mills theory is a fundamental framework in theoretical physics that describes the behavior of gauge fields. Named after physicists Chen-Ning Yang and Robert Mills, who proposed it in 1954, the theory is a cornerstone of the Standard Model of particle physics, which describes the electromagnetic, weak, and strong forces.
