Mass spectrum of type IIB flux compactifications- comments on AdS vacua and conformal dimensions

In this note we study the mass spectrum of type IIB flux compactifications. We first give a general discussion of the mass matrix for F-term vacua in four-dimensional N = 1 supergravity theories and then specialize to type IIB Calabi-Yau orientifold compactifications in the presence of geometric and non-geometric fluxes. F-term vacua in this setting are in general AdS4 vacua for which we compute the conformal dimensions of operators dual to the scalar fields. For the mirror-dual of the DGKT construction we find that one-loop corrections to the complex-structure moduli space lead to real-valued conformal dimensions - only when ignoring these corrections we recover the integer values previously reported in the literature. For an example of a flux configurations more general than the DGKT mirror we also obtain non-integer conformal dimensions. Furthermore, we argue that stabilizing the axio-dilaton and complex-structure moduli in asymptotic regions of moduli space by fluxes implies that at least one of the corresponding mass eigenvalues diverges.

Automated summary

In this note, the mass spectrum of type IIB flux compactifications is studied. The mass matrix for F-term vacua in four-dimensional N = 1 supergravity theories is discussed in general, and then specialized to type IIB Calabi-Yau orientifold compactifications with geometric and non-geometric fluxes. In this setting, F-term vacua are generally AdS4 vacua, and the conformal dimensions of operators dual to the scalar fields are computed. One-loop corrections to the complex-structure moduli space lead to real-valued conformal dimensions for the mirror-dual of the DGKT construction, while non-integer conformal dimensions are obtained for a more general flux configuration than the DGKT mirror. It is also argued that stabilizing the axio-dilaton and complex-structure moduli in asymptotic regions of moduli space by fluxes implies that at least one of the corresponding mass eigenvalues diverges.