This review provides a pedagogical overview of flux compactifications in string theory, focusing on closed string fluxes in type II theories. It begins with an introduction to the central question of finding semi-realistic four-dimensional vacua in string theory, emphasizing the need for N=1 supersymmetry with spontaneous breaking. The review discusses the historical context, including the role of Calabi-Yau manifolds and the challenges of non-Kähler geometries. It then explores no-go theorems for compactifications with fluxes, the resulting four-dimensional effective theories, and the role of fluxes in moduli stabilization. The review also covers statistical studies of flux backgrounds and the implications for the landscape of string vacua.
The paper outlines the basic definitions of type II superstring theory, including the NS-NS and RR field strengths, and their dualities. It discusses the supersymmetric solutions in the absence of flux, the conditions for supersymmetry, and the role of G-structures in flux compactifications. The review then delves into the differential conditions imposed by N=1 supersymmetry, linking torsion classes to fluxes and the resulting vacua. It presents the possible N=1 vacua in both IIA and IIB theories, highlighting the different types of solutions and their properties. The review concludes with a discussion of moduli stabilization, the role of non-perturbative effects, and the implications for de Sitter vacua. The paper emphasizes the importance of flux compactifications in achieving realistic models of particle physics and cosmology, while also addressing the challenges and open questions in the field.This review provides a pedagogical overview of flux compactifications in string theory, focusing on closed string fluxes in type II theories. It begins with an introduction to the central question of finding semi-realistic four-dimensional vacua in string theory, emphasizing the need for N=1 supersymmetry with spontaneous breaking. The review discusses the historical context, including the role of Calabi-Yau manifolds and the challenges of non-Kähler geometries. It then explores no-go theorems for compactifications with fluxes, the resulting four-dimensional effective theories, and the role of fluxes in moduli stabilization. The review also covers statistical studies of flux backgrounds and the implications for the landscape of string vacua.
The paper outlines the basic definitions of type II superstring theory, including the NS-NS and RR field strengths, and their dualities. It discusses the supersymmetric solutions in the absence of flux, the conditions for supersymmetry, and the role of G-structures in flux compactifications. The review then delves into the differential conditions imposed by N=1 supersymmetry, linking torsion classes to fluxes and the resulting vacua. It presents the possible N=1 vacua in both IIA and IIB theories, highlighting the different types of solutions and their properties. The review concludes with a discussion of moduli stabilization, the role of non-perturbative effects, and the implications for de Sitter vacua. The paper emphasizes the importance of flux compactifications in achieving realistic models of particle physics and cosmology, while also addressing the challenges and open questions in the field.