Effective Action of Matter Fields in Four-Dimensional String Orientifolds

TL;DR

The paper addresses the one-loop structure of matter-field couplings in four-dimensional Type IIB orientifolds with ${ m N}=1$ and ${ m N}=2$ sectors, focusing on the Kahler metric and couplings to twisted moduli. It combines direct string amplitudes (annulus, Möbius, and disk) with field-theory expectations to show that the infrared part of the one-loop Kahler metric reproduces the field-theory anomalous dimensions, while ${ m N}=2$ sectors generate moduli-dependent threshold corrections for untwisted directions; and it confirms, via disk amplitudes, the tree-level couplings of twisted moduli to charged matter consistent with ${ m SU}(2)_R$ symmetry, including a nonzero FI coupling for the triplet and zero coupling for the singlet in ${ m N}=2$ cases. In ${ m N}=1$ models, oscillator modes do not decouple and the IR behavior matches the anomalous dimensions with the UV cut set by the string scale $M_S$, whereas ${ m N}=2$ sectors yield explicit moduli-dependent thresholds, with the ${ m Z}_3$ case showing precise anomalous-dimension matching and the ${ m Z}_6'$ case showing absence of one-loop FI terms. The threshold corrections depend on complex-structure moduli (e.g., $U$) and appear as logarithms and Dedekind-eta function contributions, consistent with heterotic limits and requiring non-perturbative effects for full $T$-modulus dependence. Overall, the work clarifies how stringy one-loop effects shape the effective action for matter fields in orientifold compactifications and how SUSY constrains these couplings.

Abstract

We study various aspects of the Kahler metric for matter fields in N=1,2 orientifold compactifications of type IIB string theory. The result has an infrared-divergent part which reproduces the field- theoretical anomalous dimensions, and a moduli-dependent part which comes from N=2 sectors of the orientifold. For the N=2 orientifolds, we also compute the disk amplitude for two matter fields on the boundary and a twisted closed string modulus in the bulk. Our results are in agreement with supersymmetry: the singlet under the SU(2)_R R-symmetry has vanishing coupling, while the coupling of the SU(2)_R triplet does not vanish.