On the 4D effective theory in warped compactifications with fluxes and branes

TL;DR

This paper develops a systematic method to derive four-dimensional effective theories from ten-dimensional type IIB supergravity with fluxes and branes, accounting for backreaction effects on warped geometries.

Contribution

It introduces a gradient expansion approach to obtain consistent 4D effective equations from 10D supergravity with fluxes and branes, including backreaction effects.

Findings

Derived 4D effective equations incorporating backreaction.

Provided a systematic method for warped compactifications with fluxes and branes.

Enabled analysis of moduli, branes, and flux dynamics in 4D.

Abstract

We present a systematic way to derive the four-dimensional effective theories for warped compactifications with fluxes and branes in the ten-dimensional type IIB supergravity. The ten-dimensional equations of motion are solved using the gradient expansion method and the effective four-dimensional equations of motions are derived by imposing the consistency condition that the total derivative terms with respect to the six-dimensional internal coordinates vanish when integrated over the internal manifold. By solving the effective four-dimensional equations, we can find the gravitational backreaction to the warped geometry due to the dynamics of moduli fields, branes and fluxes.