BreakingCPTby mixed noncommutativity

The mixed component of the noncommutative parameter ${\theta }_{\mu M},$ where $\mu =0,1,2,3\mathrm{}$ and M is an extra dimensional index, may violate four-dimensional $\mathrm{CPT}$ invariance. We calculate one- and two-loop induced couplings of ${\theta }_{\mu 5}$ with the four-dimensional axial vector current and with the $\mathrm{CPT}$ odd $\dim =6\mathrm{}$ operators starting from five-dimensional Yukawa and $U\left(1\right)\mathrm{}$ theories. The resulting bounds from clock comparison experiments place a stringent constraint on ${\theta }_{\mu 5},$ $|{\theta }_{\mu 5}{|}^{-1/2}\gtrsim 5\times {10}^{11}\hspace{0.5em}\mathrm{GeV}.$ Orbifold projection and/or localization of fermions on a 3-brane lead to $\mathrm{CPT}$-conserving physics, in which case the constraints on ${\theta }_{\mu 5}$ are softened.