Dynamical D4-D8 and D3-D7 branes in supergravity

TL;DR

This paper constructs and analyzes dynamical intersecting D4-D8 and D3-D7 brane solutions in supergravity, exploring their lower-dimensional effective descriptions, geometric properties, and cosmological implications.

Contribution

It introduces new dynamical solutions for intersecting branes in supergravity and examines their geometric structure and cosmological behavior, highlighting limitations of effective lower-dimensional descriptions.

Findings

D4-D8 solutions reduce to static warped AdS_6 x S^4 geometry in certain regions.

D3-D7 solutions exhibit dynamical metrics similar to D3-branes with nontrivial dilaton.

Solutions behave like Kasner cosmology at late times and static warped geometries at early times.

Abstract

We present a class of dynamical solutions for intersecting D4-D8 and D3-D7 brane systems in ten-dimensional type IIA and IIB supergravity. We discuss if these solutions can be recovered in lower-dimensional effective theories for the warped compactification of a general p-brane system. It is found that an effective $p+1$-dimensional description is not possible in general due to the entanglement of the transverse coordinates and the $p+1$-dimensional coordinates in the metric components. For the D4-D8 brane system, the dynamical solutions reduces to a static warped ${\rm AdS_6}\times {\rm S}^4$ geometry in a certain spacetime region. For the D3-D7 brane system, we find a dynamical solution whose metric form is similar to that of a D3-brane solution. The main difference is the existence of a nontrivial dilaton configuration in the D3-D7 solution. Then we discuss cosmology of these solutions. We find that they behave like a Kasner-type cosmological solution at $\tau\to\infty$, while it reduces to a warped static solution at $\tau\to0$, where $\tau$ is the cosmic time.