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

The Kähler potential is the least understood part of effective N = 1 supersymmetric theories derived from string compactifications. Even at tree-level, the Kähler 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 Kähler moduli. Scaling arguments, locality and knowledge of the structure of the physical Yukawa couplings are sufficient to find the relevant Kähler 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 Kähler potential, but are sufficient to extract relevant information about the canonically normalised matter fields and the soft supersymmetry breaking terms in gravity mediated scenarios.