The Universal Kaehler Modulus in Warped Compactifications

TL;DR

This work addresses how the universal Kaehler modulus behaves in warped flux compactifications and whether warping alters the 4d Kahler potential. Using a Hamiltonian (gauge-invariant) approach to 10d supergravity, the authors derive linear and nonlinear 10d fluctuations for the universal volume modulus and its axionic partner, show that warping effects cancel in the kinetic terms up to an additive shift in the background modulus, and prove no kinetic mixing with light KK modes, even in strongly warped throats. They obtain a closed-form no-scale Kahler potential K = -3 log(-i(ρ-ρ̄) + 2 V_W^0 / V_{CY}) (equivalently K = -3 log(-i(ρ-ρ̄)) after a shift), demonstrating that warping preserves no-scale structure while producing a nontrivial 10d wavefunction. A nonlinear 10d solution confirms the linear results and provides a consistent framework for modulus cosmology, with implications for KKLT-type scenarios and moduli brane couplings. The findings imply that warped compactifications admit controlled 4d effective theories for moduli without introducing warping-induced corrections to the Kahler potential, thereby supporting phenomenological uses in string cosmology and model-building.

Abstract

We construct the effective theory of the universal Kaehler modulus in warped compactifications using the Hamiltonian formulation of general relativity. The spacetime dependent 10d solution is constructed at the linear level for both the volume modulus and its axionic partner, and nontrivial cancellations of warping effects are found in the dimensional reduction. Our main result is that the Kaehler potential is not corrected by warping, up to an overall shift in the background value of the volume modulus. We extend the analysis beyond the linearized approximation by computing the fully backreacted 10d metric corresponding to a finite volume modulus fluctuation. Also, we discuss the behavior of the modulus in strongly warped regions and show that there are no mixings with light Kaluza-Klein modes. These results are important for the phenomenology and cosmology of flux compactifications.