T-parity violation by anomalies

Little Higgs theories often rely on an internal parity (“$T$-parity”) to suppress nonstandard electroweak effects or to provide a dark matter candidate. We show that such a symmetry is generally broken by anomalies, as described by the Wess-Zumino-Witten term. We study a simple $SU(3)\times SU(3)/SU(3)$ Little Higgs scheme where we obtain a minimal form for the topological interactions of a single Higgs field. The results apply to more general models, including $[SU(3)\times SU(3)/SU(3){]}^4$, $SU(5)/SO(5)$, and $SU(6)/Sp(6)$.