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Dynamics of Warped Flux Compactifications

Gary Shiu, Gonzalo Torroba, Bret Underwood, Michael R. Douglas

TL;DR

This work derives a comprehensive 4d effective action for warped type IIB flux compactifications by performing a 10d-to-4d reduction in an axial gauge, and by carefully solving the resulting constraints. It demonstrates that, to quadratic order, the warped moduli kinetic terms decouple from KK modes and yields a warped Kähler potential for metric fluctuations, while exhibiting a warped GVW-type flux potential that generalizes moduli stabilization in ISD backgrounds. The analysis reveals geometric KK masses that persist in warped geometries, a warped Higgs-like mechanism coupling gravitons to internal-metric KK modes, and selective flux-induced lifting of complex moduli and axio-dilaton with no mixing with p-forms at leading order. These results provide a concrete framework for warped effective theories with applications to moduli stabilization (e.g., KKLT), warped inflation scenarios, SUSY breaking mediation, and phenomenology of warped throats. Overall, the paper clarifies how warping reshapes the 4d effective action, moduli dynamics, and flux-induced potentials, with implications for both fundamental theory and cosmological model-building.

Abstract

We discuss the four dimensional effective action for type IIB flux compactifications, and obtain the quadratic terms taking warp effects into account. The analysis includes both the 4-d zero modes and their KK excitations, which become light at large warping. We identify an `axial' type gauge for the supergravity fluctuations, which makes the four dimensional degrees of freedom manifest. The other key ingredient is the existence of constraints coming from the ten dimensional equations of motion. Applying these conditions leads to considerable simplifications, enabling us to obtain the low energy lagrangian explicitly. In particular, the warped Kähler potential for metric moduli is computed and it is shown that there are no mixings with the KK fluctuations and the result differs from previous proposals. The four dimensional potential contains a generalization of the Gukov-Vafa-Witten term, plus usual mass terms for KK modes.

Dynamics of Warped Flux Compactifications

TL;DR

This work derives a comprehensive 4d effective action for warped type IIB flux compactifications by performing a 10d-to-4d reduction in an axial gauge, and by carefully solving the resulting constraints. It demonstrates that, to quadratic order, the warped moduli kinetic terms decouple from KK modes and yields a warped Kähler potential for metric fluctuations, while exhibiting a warped GVW-type flux potential that generalizes moduli stabilization in ISD backgrounds. The analysis reveals geometric KK masses that persist in warped geometries, a warped Higgs-like mechanism coupling gravitons to internal-metric KK modes, and selective flux-induced lifting of complex moduli and axio-dilaton with no mixing with p-forms at leading order. These results provide a concrete framework for warped effective theories with applications to moduli stabilization (e.g., KKLT), warped inflation scenarios, SUSY breaking mediation, and phenomenology of warped throats. Overall, the paper clarifies how warping reshapes the 4d effective action, moduli dynamics, and flux-induced potentials, with implications for both fundamental theory and cosmological model-building.

Abstract

We discuss the four dimensional effective action for type IIB flux compactifications, and obtain the quadratic terms taking warp effects into account. The analysis includes both the 4-d zero modes and their KK excitations, which become light at large warping. We identify an `axial' type gauge for the supergravity fluctuations, which makes the four dimensional degrees of freedom manifest. The other key ingredient is the existence of constraints coming from the ten dimensional equations of motion. Applying these conditions leads to considerable simplifications, enabling us to obtain the low energy lagrangian explicitly. In particular, the warped Kähler potential for metric moduli is computed and it is shown that there are no mixings with the KK fluctuations and the result differs from previous proposals. The four dimensional potential contains a generalization of the Gukov-Vafa-Witten term, plus usual mass terms for KK modes.

Paper Structure

This paper contains 25 sections, 118 equations, 1 table.

Table of Contents

  1. Introduction
  2. Review of GKP ansatz
  3. Towards an effective description of warping
  4. Some applications of warped effective theories
  5. Summary of the paper
  6. From 10 to 4: Warped Fluctuations and Effective Action
  7. 10d perspective for fluctuations in IIB supergravity
  8. Ten dimensional fluctuated equations
  9. Four dimensional effective action
  10. Warped Kinetic Terms and Moduli Space Metrics
  11. Axio-dilaton and $p$-form modes
  12. Graviton fluctuations
  13. Kähler potential for internal metric fluctuations
  14. Supersymmetry considerations
  15. Geometric Masses for KK modes
  16. ...and 10 more sections