Low-energy Limits on the Antisymmetric Tensor Field Background on the   Brane and on the Non-commutative Scale
  A non-vanishing vacuum expectation value for an antisymmetric tensor field leads to the violation of Lorentz invariance on the brane. This violation is controlled by the $\theta_{\mu \nu}$ parameter, which has a dimension of inverse mass squared. We assume that the zeroth order term in theta-expansion represents the Standard Model and study the effects induced by linear terms in theta_{\mu\nu}. Low-energy precision experiments place the limit on the possible size of this background at the level of $1/\sqrt{\theta} > 5 \times 10^{14}$ GeV. This poses certain difficulty for the TeV-range string scale models, in which the antisymmetric field has to acquire a relatively large mass to ensure that $\theta_{\mu \nu}=0$ and avoid cosmological moduli problem. 
Irina Mocioiu, Maxim Pospelov and Radu Roiban