Dynamics of Warped Flux Compactifications

TL;DR

This paper derives the four-dimensional effective action for warped flux compactifications in type IIB string theory, explicitly computing the warped Kähler potential and clarifying the role of KK modes and constraints from 10D equations.

Contribution

It provides a detailed derivation of the 4D effective action including warp effects, and computes the warped Kähler potential, correcting previous assumptions about mode mixing.

Findings

Warped Kähler potential differs from previous proposals.

KK modes are light at large warping but do not mix with metric moduli.

The 4D potential includes a generalized Gukov-Vafa-Witten term.

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 K\"ahler 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.