Gauge symmetries decrease the number of Dp-brane dimensions

It is known that the presence of the antisymmetric background field B-mu nu leads to the noncommutativity of the Dp-brane manifold. The addition of the linear dilaton field in the form Phi(x)=Phi(0)+a(mu)x(mu) causes the appearance of the commutative Dp-brane coordinate x=a(mu)x(mu). In the present article we show that for some particular choices of the background fields, a(2)equivalent to G(mu nu)a(mu)a(nu)=0 and a(2)equivalent to[(G-4BG(-1)B)(-1)](mu nu)a(mu)a(nu)=0, the local gauge symmetries appear in the theory. They turn some Neuman boundary conditions into the Dirichlet ones, and consequently decrease the number of the Dp-brane dimensions.