Universal properties of type IIB and F-theory flux compactifications at large complex structure

Abstract

Abstract:We consider flux compactifications of type IIB string theory and F-theory in which the respective superpotentials at large complex structure are dominated by cubic or quartic terms in the complex structure moduli. In this limit, the low-energy effective theory exhibits universal properties that are insensitive to the details of the compactification manifold or the flux configuration. Focussing on the complex structure and axio-dilaton sector, we show that there are no vacua in this region and the spectrum of the Hessian matrix is highly peaked and consists only of three distinct eigenvalues (0, 2m 2 3/2 and 8m 2 3/2 ), independently of the number of moduli. We briefly comment on how the inclusion of Kähler moduli affect these findings. Our results generalise those of Brodie & Marsh [1], in which these universal properties were found in a subspace of the large complex structure limit of type IIB compactifications.

Towards a complete mass spectrum of type-IIB flux vacua at large complex structure

“…Regarding the validity of the statistical methods, our numerical scan shows a deficit in the number of generic no-scale vacua with respect to the theoretical statistical distributions in a small neighbourhood of the LCS point. This is in perfect agreement with previous analyses which predict a breakdown of the continuous flux approximation in this limit [15,[68][69][70]. The failure of this approximation leads to an absence of generic no-scale vacua in the LCS limit [71] of one-parameter models, other than the vacuum sitting on the LCS point itself [72] (see also [73]).…”

“…The real parameter ξ ∈ [0, 1/2] depends on the configuration of the complex structure of the reduced theory, and in particular it takes the value ξ = 0 at the LCS point. Analogous universal properties of the spectrum of matrices arising in the effective theory were previously reported in [67,68], where the authors considered generic points of the moduli space, i.e., not necessarily flux vacua. The computations of the mass spectra rely on the perturbative description of the moduli space geometry at large complex structure, and thus are valid provided the exponentially suppressed instanton corrections can be neglected.…”

“…only assume that the exponentially suppressed instanton contributions to the prepotential (2.10) can be entirely neglected. Therefore, the results presented below generalize those of [68,91,92], as the regime of validity of our analysis can be extended to the entire region of the moduli space where the polynomial approximation of the prepotential (2.10) is under control.…”

“…The argument below will proceed along the lines of [68,91,92], where analogous properties for the Yukawas where found strictly at the LCS point (ξ = 0). But here we will…”

Inflation with a graceful exit in a random landscape

“…Though this approximation is very restrictive and fails to incorporate some of the rich structure of the string landscape [2,3,[12][13][14][15][16][17], we argue that it still retains some fundamental features that allow for a qualitative understanding of the landscape's…”