Remarks on the Effects of Quantum Corrections on Moduli Stabilization and de Sitter Vacua in Type IIB String Theory

The role of string loop corrections on the existence of de Sitter vacua and the moduli stabilization problem is examined in type IIB effective theories. The fundamental building blocks are a minimum of three intersecting D7 brane stacks, three Kähler moduli, and a novel Einstein-Hilbert term associated with higher derivative terms of the 10-dimensional effective action. It was shown in previous works that loop corrections appear which induce novel logarithmic volume-dependent terms in the effective potential. When D-term contributions are considered, all Kähler moduli are stabilized and de Sitter vacua are achieved. In the present work, a comprehensive study of multiple non-perturbative terms in the superpotential is undertaken. The combined effects of the logarithmic loop corrections and two non-perturbative superpotential Kaehler moduli dependent terms have been investigated. It is shown that a variety of fluxes exist for large as well as moderate volume compactifications which define a de Sitter space and stabilize the moduli fields. For large volumes, a generic simple form of the potential is achieved. The so obtained effective potential appears to be promising for cosmological applications.