Extended No-Scale Structure and ${\alpha }^{{}^{\prime }2}$ Corrections to the Type IIB Action

Abstract

We analyse a new $\mathcal{N}=1$ string tree level correction at $\mathcal{O}({\alpha }^{\prime 2})$ to the Kähler potential of the volume moduli of type IIB Calabi-Yau flux compactification found recently by Grimm, Savelli and Weissenbacher~\cite{Grimm:2013gma} and its impact on the moduli potential. We find that it imposes a strong lower bound the Calabi-Yau volume in the Large Volume Scenario of moduli stabilisation. For KKLT-like scenarios we find that consistency of the action imposes an upper bound on the flux superpotential $|W_0|\lesssim 10^{-3}$, while parametrically controlled survival of the KKLT minimum needs extreme tuning of $W_0$ close to zero. We also analyse the Kähler uplifting mechanism showing that it can operate on Calabi-Yau manifolds where the new correction is present and dominated by the 4-cycle controlling the overall volume if the volume is stabilised at values $\mathcal{V}\gtrsim 10^3$. We discuss the phenomenological implication of these bounds on $\mathcal{V}$ in the various scenarios.

arXiv comment26 pages, 1 figure