SUNTrace[exp] is the head of color traces. By default
the trace is not evaluated. The evaluation occurs only when the option
SUNTraceEvaluate is set to True. It is
recommended to use SUNSimplify, which will automatically
evaluate all color traces involving 2 or 3 matrices in the input
expression.
Overview, SUNSimplify, SUNT, SUNTF, SUNF, SUND, SUNTraceEvaluate.
SUNTrace[SUNT[a, b]]\text{tr}\left(T^a.T^b\right)
SUNTrace[SUNT[a, b], SUNTraceEvaluate -> True]\frac{\delta ^{ab}}{2}
SUNTrace[SUNT[a, b]] // SUNSimplify\frac{\delta ^{ab}}{2}
SUNTrace[SUNT[a, b, c]] // SUNSimplify\frac{d^{abc}}{4}+\frac{1}{4} i f^{abc}
SUNTrace[SUNT[a, b, c, d]] // SUNSimplify[#, SUNTraceEvaluate -> True, SUNIndexNames -> {j}] &\frac{1}{4} \delta ^{ad} \left(C_A-2 C_F\right) \delta ^{bc}-\frac{1}{4} \delta ^{ac} \left(C_A-2 C_F\right) \delta ^{bd}+\frac{1}{4} \delta ^{ab} \left(C_A-2 C_F\right) \delta ^{cd}-\frac{1}{8} i f^{adj} d^{bcj}+\frac{1}{8} i d^{adj} f^{bcj}+\frac{1}{8} d^{adj} d^{bcj}-\frac{1}{8} d^{bdj} d^{acj}+\frac{1}{8} d^{cdj} d^{abj}
SUNTrace[SUNT[a, b, c, a, b, c]] // SUNSimplify\frac{1}{4} \left(C_A^2+1\right) C_F \left(C_A-2 C_F\right)