Gauge symmetries decrease the number of Dp-brane dimensions

TL;DR

The paper demonstrates that specific gauge symmetries arising from particular background fields can reduce the effective dimensions of Dp-branes by transforming boundary conditions.

Contribution

It reveals how gauge symmetries induced by certain background fields can alter boundary conditions, decreasing Dp-brane dimensions.

Findings

Gauge symmetries appear under specific background field conditions.

Boundary conditions change from Neumann to Dirichlet due to gauge symmetries.

Number of Dp-brane dimensions decreases as a result.

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 $\tilde a^2\equiv [ (G-4BG^{-1}B)^{-1}\ ]^{\mu\nu}a_\mu a_\nu=0$, 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.