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

Daniel Baumann, Anatoly Dymarsky, Igor R. Klebanov, Juan Maldacena, Liam McAllister, Arvind Murugan

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.

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

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.

Paper Structure

This paper contains 35 sections, 152 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Motivation
  3. Method
  4. Outline
  5. D3-branes and Volume Stabilization
  6. Nonperturbative Volume Stabilization
  7. D3-brane Potential After Volume Stabilization
  8. Warped Volumes and the Superpotential
  9. The Role of the Warped Volume
  10. Corrections to the Warped Volumes of Four-Cycles
  11. D3-brane Backreaction
  12. The Green's Function Method
  13. Comparison with the Open-String Approach
  14. A Model for the Four-Cycles
  15. Backreaction in Warped Conifold Geometries
  16. ...and 20 more sections

Figures (1)

  • Figure 1: Cartoon of an embedded stack of D7-branes wrapping a four-cycle $\Sigma_4$, and a mobile D3-brane, in a warped throat region of a compact Calabi-Yau. In the scenario of KKLMMT the D3-brane feels a force from an anti-D3-brane at the tip of the throat. Alternatively, in Dymarsky:2005xt it was argued that a D3-brane in the resolved warped deformed conifold background feels a force even in the absence of an anti-D3-brane. In this paper we consider an additional contribution to the D3-brane potential, coming from nonperturbative effects on D7-branes.