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

TL;DR

This paper investigates a new correction to the type IIB string theory effective action, revealing bounds on Calabi-Yau volume and flux superpotential that influence moduli stabilization scenarios and phenomenology.

Contribution

It identifies a novel ${ m O}(\a'^2)$ correction to the K"ahler potential and analyzes its effects on volume bounds and flux tuning in moduli stabilization.

Findings

Imposes a lower bound on Calabi-Yau volume in LVS.

Sets an upper bound on flux superpotential $|W_0|\lesssim 10^{-3}$ in KKLT.

Shows K"ahler uplifting can work with the correction at large volumes.

Abstract

We analyse a new ${\cal N}=1$ string tree level correction at ${\cal O}(\alpha'^2)$ to the K\"ahler 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 K\"ahler 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.