Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 305 / 4 / c / Solution

The QCD Yang-Mills theta term isThe chromoelectric field is a spatial vector and the chromomagnetic field is a pseudovector, so their scalar product is odd under parity. It is also odd under time-reversal symmetry because time reversal reverses ${\mathbf{B}}^A$ but not ${\mathbf{E}}^A$. Charge conjugation reverses both color fields in the gauge-invariant trace and leaves the product even. The term therefore violates P, T, and CP, while it preserves CPT because the two sign reversals from P and T cancel.