Field redefinitions and K\"ahler potential in string theory at 1-loop

TL;DR

This paper derives the structure of field redefinitions and the K"ahler potential at 1-loop in certain string theory models, clarifying how supersymmetry constrains low-energy effective actions and identifying which terms require explicit string amplitude calculations.

Contribution

It provides a general framework for 1-loop field redefinitions and K"ahler potential in 4D toroidal type IIB orientifolds with ${ m N}=1$ supersymmetry, using symmetry principles and an ansatz.

Findings

Derived the structure of 1-loop field redefinitions.

Identified the form of the K"ahler potential at 1-loop.

Highlighted which terms need explicit string amplitude calculations.

Abstract

Field redefinitions at string 1-loop order are often required by supersymmetry, for instance in order to make the K\"ahler structure of the scalar kinetic terms manifest. We derive the general structure of the field redefinitions and the K\"ahler potential at string 1-loop order in a certain class of string theory models (4-dimensional toroidal type IIB orientifolds with ${\cal N}=1$ supersymmetry) and for a certain subsector of fields (untwisted K\"ahler moduli and the 4-dimensional dilaton). To do so we make use of supersymmetry, perturbative axionic shift symmetries and a particular ansatz for the form of the 1-loop corrections to the metric on the moduli space. Our results also show which terms in the low-energy effective action have to be calculated via concrete string amplitudes in order to fix the values of the coefficients (in the field redefinitions and the K\"ahler potential) that are left undetermined by our general analysis based on (super)symmetry.