Kinetic terms in warped compactifications

TL;DR

This paper develops a formalism to compute the kinetic terms of 4d fields in warped string compactifications, using a Hamiltonian approach to account for gauge dependence and warping effects.

Contribution

It introduces a gauge-dependent inner product framework for kinetic terms in warped compactifications and applies it to the Klebanov-Strassler solution.

Findings

Confirmed the qualitative impact of warping on kinetic terms.

Quantitative results differ from previous power-like divergence estimates.

Provided a new method for calculating kinetic terms in warped backgrounds.

Abstract

We develop formalism for computing the kinetic terms of 4d fields in string compactifications, particularly with warping. With the help of the Hamiltonian approach, we identify a gauge dependent inner product on the compactification manifold which depends on the warp factor. It is shown that kinetic terms are associated to the minimum value of the inner product over each gauge orbit. We work out the kinetic term for the complex modulus of a deformed conifold with flux, i.e. the Klebanov-Strassler solution embedded in a compact Calabi-Yau manifold. Earlier results of a power-like divergence are confirmed qualitatively (the kinetic term does contain the main effect of warping) but not quantitatively (the correct results differ by an order one coefficient).