Remarks on the effects of quantum corrections on moduli stabilization and de Sitter vacua in type IIB string theory

The r\^ole 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 K\"ahler 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 K\"ahler 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 K\"ahler 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.