Kahler Potentials of Chiral Matter Fields for Calabi-Yau String Compactifications

TL;DR

This work tackles the problem of determining the Kähler metric for chiral matter fields in Calabi–Yau flux compactifications, which is crucial for canonical normalisation and soft terms but remains poorly understood. The authors develop a method that leverages the perturbative shift symmetry forbidding Kähler moduli from appearing in the tree-level superpotential, allowing the modular dependence of the matter metric to be inferred from the scaling of physical Yukawa couplings via $\\hat{Y}_{\\alpha\\beta\\gamma} = e^{K/2} Y_{\\alpha\\beta\\gamma} /(\\tilde{K}_{\\alpha}\\tilde{K}_{\\beta}\\tilde{K}_{\\gamma})^{1/2}$. Applying this to IIB flux compactifications with magnetised D7 branes in the large-volume regime yields a universal volume scaling $\\tilde{K}_{\\alpha} \sim \tau_b^{-1} k_{\\alpha}(\\phi)$ and determines small-cycle exponents for several local geometries, including cases with minimal and more complex intersections. The results, which also reproduce toroidal calculations, provide a practical framework to estimate soft terms in gravity-mediated SUSY breaking and clarify how local brane geometry controls matter metrics in a controlled, weak-coupling expansion. The approach has clear phenomenological relevance for MSSM-like sectors in string models and clarifies the limitations related to moduli that do and do not appear in the superpotential.

Abstract

The Kahler potential is the least understood part of effective N=1 supersymmetric theories derived from string compactifications. Even at tree-level, the Kahler potential for the physical matter fields, as a function of the moduli fields, is unknown for generic Calabi-Yau compactifications and has only been computed for simple toroidal orientifolds. In this paper we describe how the modular dependence of matter metrics may be extracted in a perturbative expansion in the Kahler moduli. Scaling arguments, locality and knowledge of the structure of the physical Yukawa couplings are sufficient to find the relevant Kahler potential. Using these techniques we compute the `modular weights' for bifundamental matter on wrapped D7 branes for large-volume IIB Calabi-Yau flux compactifications. We also apply our techniques to the case of toroidal compactifications, obtaining results consistent with those present in the literature. Our techniques do not provide the complex structure moduli dependence of the Kahler potential, but are sufficient to extract relevant information about the canonically normalised matter fields and the soft supersymmetry breaking terms in gravity mediated scenarios.