Constraints on background torsion field from K physics

We point out that a background torsion field will produce an effective potential to the K and K̄ with opposite signs. This allows us to constrain the background torsion field from the KL and KS mass difference, CPT violating K ◦ and K̄ mass difference and the CP violating quantities ǫ and η+−. The most stringent bound on the cosmological background torsion 〈T 0〉 < 10−25 GeV comes from the direct measurement of the CPT violation. General Theory of relativity has so far succeeded in confronting all experimental tests. However the problem of quantising gravity leads one to believe that Einsteins theory though correct may not be the most general theory which describes the dynamics of the metric tensor and its interactions with matter. The ultimate quantum theory of gravity must also explain the low energy phenomenology. This gave rise to the birth of string theory, which is now considered as the most consistent theory of quantum gravity. In string theory the metric tensor field comes out naturally and gives the response of matter to this metric. However, it also predicts several other fields like the antisymmetric second rank field, which enters via its antisymmetrized derivatives, Tαβγ = ∂[αAβγ], which are usually referred to as the torsion field. In addition to the string inspired approach to study the torsion dynamics, there are some modifications of the GTR where connection is treated as more fundamental than the metric. In a metric compatible theory of gravity one generalizes the connection by including the torsion tensor [1, 2]. The symmetric part of the generalized connection are the Christoffel symbols given by the usual formula in terms of the metric, whereas the torsion is the antisymmetric part of the connection which in Einsteins gravity is assumed to be zero. The coupling of the matter fields to torsion arises from the covariant derivative with respect to the generalized connection . The covariant derivative of a fundamental scalar field is just the partial derivative therefore the torsion term does not couple to scalars . The torsion field also does not couple to electro-magnetic fields as the gauge invariant field strength is the antisymmetric partial derivative,Fμν ≡ (dA)μν = ∂μAν−∂νAμ . This is the general definition for the field strength even in curved space. If one were to generalise the definition of Fμν by replacing the partial derivatives with the covariant derivative (4), the extra terms involving torsion will not be gauge invariant. Coupling of the electro-magnetic field with torsion can only arise in some more generalized versions of torsion theories [3].