Gauge symmetries decrease the number of Dp-brane dimensions. II. Inclusion of the Liouville term

TL;DR

This paper explores how including the Liouville term in string theory with background fields affects gauge symmetries and the effective dimensions of Dp-branes, revealing new conditions for dimensional reduction.

Contribution

It extends previous work by analyzing the impact of the Liouville term on gauge symmetries and Dp-brane dimensions in the presence of background fields.

Findings

Gauge symmetries can convert Neumann to Dirichlet boundary conditions.

The number of Dp-brane dimensions decreases under certain background field relations.

Conformal invariance is maintained with the Liouville term, depending on the central charge.

Abstract

The presence of the antisymmetric background field $B_{\mu\nu}$ leads to the noncommutativity of the Dp-brane manifold, while the linear dilaton field in the form $\Phi(x)=\Phi_0+a_\mu x^\mu$, causes the appearance of the commutative Dp-brane coordinate, $x_c=a_\mu x^\mu$. In the present article we consider the case where the conformal invariance is realized by inclusion of the Liouville term. Then, the theory is conformally invariant even in the presence of the world sheet conformal factor $F$, and it depends on the new parameter, the central charge $c$. As well as in the absence of the Liouville action, for particular relations between background fields, the local gauge symmetries appear in the theory. They turn some Neumann boundary conditions into the Dirichlet ones, and decrease the number of the Dp-brane dimensions.