Towards p-Adic String in Constant B-Field

Spacetime properties of the tachyon of the p-adic string theory can be derived from a (non-local) action on the p-adic line Q_p, thought of as the boundary of the `worldsheet’. We show that a term corresponding to the background of the antisymmetric second rank tensor field B can be added to this action. We examine the consequences of this term, in particular, its relation to a noncommutative deformation of the effective theory of the p-adic tachyon in spacetime.