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We discuss prospects for stabilizing the volume modulus of N = 1 supersymmetric type IIB orientifold compactifications using only perturbative corrections to the Kähler potential. Concretely, we consider the known string loop corrections and tree-level alpha' corrections. They break the no-scale structure of the potential, which otherwise prohibits stabilizing the volume modulus. We argue that when combined, these corrections provide enough flexibility to stabilize the volume of the internal space without nonperturbative effects, although we are not able to present a completely explicit example within the limited set of currently available models. Furthermore, a certain amount of fine-tuning is needed to obtain a minimum at large volume.
Berg et al. (Thu,) studied this question.