Gauge symmetries decrease the number of Dp-brane dimensions

Abstract

It is known that the presence of antisymmetric background field $B_{μν}$ leads to noncommutativity of Dp-brane manifold. Addition of the linear dilaton field in the form $Φ(x)=Φ_0+a_μx^μ$, causes the appearance of the commutative Dp-brane coordinate $x=a_μx^μ$. In the present article we show that for some particular choices of the background fields, $a^2\equiv G^{μν}a_μa_ν=0$ and $\tilde a^2\equiv [ (G-4BG^{-1}B)^{-1}\ ]^{μν}a_μa_ν=0$, 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.