Can we live on a D-brane? -- Effective theory on a self-gravitating D-brane --

TL;DR

This paper derives the effective gravitational theory on a self-gravitating D-brane in type IIB supergravity, showing the equivalence of holographic and geometrical methods and highlighting the non-appearance of Maxwell fields in the low-order effective theory.

Contribution

It provides a detailed derivation of the effective theory on a D-brane using two methods and clarifies the nature of the resulting gravitational equations.

Findings

Effective equations on the D-brane from holographic and geometrical methods coincide.

The Born-Infeld action does not lead to Einstein-Maxwell theory at low order.

Careful analysis is needed for cosmological models on self-gravitating D-branes.

Abstract

We consider a D-brane coupled with gravity in type IIB supergravity on S^5 and derive the effective theory on the D-brane in two different ways, that is, holographic and geometrical projection methods. We find that the effective equations on the brane obtained by these methods coincide. The theory on the D-brane described by the Born-Infeld action is not like Einstein-Maxwell theory in the lower order of the gradient expansion, i.e., the Maxwell field does not appear in the theory. Thus the careful analysis and statement for cosmology on self-gravitating D-brane should be demanded in realistic models.