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 θμν parameter, which has a dimension of inverse mass squared. We assume that the zeroth order term in θ-expansion represents the Standard Model and study the effects induced by linear terms in θμν. Low-energy precision experiments place the limit on the possible size of this background at the level of 1/θ≳5 ×1014 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 θμν=0 and avoid cosmological moduli problem.