Gauge symmetries decrease the number of Dp-brane dimensions

Abstract

It is known that the presence of antisymmetric background field $B_{\mu \nu }$ leads to noncommutativity of Dp-brane manifold. 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, $a^2\equiv G^{\mu \nu }{a}_{\mu }{a}_{\nu }=0$ and ${\tilde{a}}^2\equiv [(G-4B{G}^{-1}B{)}^{-1}{]}^{\mu \nu }{a}_{\mu }{a}_{\nu }=0$, 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.

We improve Sec.4. and Conclusion and we added the Appendix in order to clarify results

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