On D3-brane Potentials in Compactifications with Fluxes and Wrapped D-branes

TL;DR

This paper analyzes the potential experienced by D3-branes in warped flux compactifications, computing loop corrections to the superpotential and exploring implications for string cosmology and inflation models.

Contribution

It provides explicit calculations of D3-brane potentials including loop corrections in warped backgrounds, linking geometric embeddings to superpotential modifications.

Findings

Superpotential corrections are given by the embedding equations of wrapped four-cycles.

The approach solves the holomorphic gauge coupling problem on wrapped D7-branes.

Results are applicable to D3-brane inflation scenarios in warped throats.

Abstract

We study the potential governing D3-brane motion in a warped throat region of a string compactification with internal fluxes and wrapped D-branes. If the Kahler moduli of the compact space are stabilized by nonperturbative effects, a D3-brane experiences a force due to its interaction with D-branes wrapping certain four-cycles. We compute this interaction, as a correction to the warped four-cycle volume, using explicit throat backgrounds in supergravity. This amounts to a closed-string channel computation of the loop corrections to the nonperturbative superpotential that stabilizes the volume. We demonstrate for warped conical spaces that the superpotential correction is given by the embedding equation specifying the wrapped four-cycle, in agreement with the general form proposed by Ganor. Our approach automatically provides a solution to the problem of defining a holomorphic gauge coupling on wrapped D7-branes in a background with D3-branes. Finally, our results have applications to cosmological inflation models in which the inflaton is modeled by a D3-brane moving in a warped throat.