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

Abstract

The large number of moduli fields arising in a generic string theory compactification makes a complete computation of the low energy effective theory infeasible. A common strategy to solve this problem is to consider Calabi-Yau manifolds with discrete symmetries, which effectively reduce the number of moduli and make the computation of the truncated Effective Field Theory possible. In this approach, however, the couplings (e.g., the masses) of the truncated fields are left undetermined. In the present paper we discuss the tree-level mass spectrum of type-IIB flux compactifications at Large Complex Structure, focusing on models with a reduced one-dimensional complex structure sector. We compute the tree-level spectrum for the dilaton and complex structure moduli, including the truncated fields, which can be expressed entirely in terms of the known couplings of the reduced theory. We show that the masses of this set of fields are naturally heavy at vacua consistent with the KKLT construction, and we discuss other phenomenologically interesting scenarios where the spectrum involves fields much lighter than the gravitino. We also derive the probability distribution for the masses on the ensemble of flux vacua, and show that it exhibits universal features independent of the details of the compactification. We check our results on a large sample of flux vacua constructed in an orientifold of the Calabi-Yau $$ {\mathbbm{W}\mathrm{\mathbb{P}}}_{\left[1,1,1,1,4\right]}^4 $$ W ℙ 1 1 1 1 4 4 . Finally, we also discuss the conditions under which the spectrum derived here could arise in more general compactifications.

F-theory flux vacua at large complex structure

“…In our scheme, the mass spectrum clearly depends on the correction K (3) , as one of the fields is only stabilised when they are taken into account. This is also consistent with the results of [45,48], since the parameter ξ that controls their mass spectrum is a simple function of K (3) . Furthermore, we also showed that in one particular case in which the matrix M is not invertible, we recover the residual flat direction found in [47] for the same flux choices.…”

“…The analysis presented in this paper offers some avenues to follow in the future: first of all it would be interesting to calculate the precise mass spectra for the F-theory vacua obtained here as done in [45,48] for the type IIB case. In this way one could verify whether there is indeed a hierarchy between the masses of the fields in the complex structure sector.…”

“…For altenative definitions of flux-axion invariants in the type IIB compactifications see[26,45,46].…”

F-theory flux vacua at large complex structure

“…In our scheme, the mass spectrum clearly depends on the correction K (3) , as one of the fields is only stabilised when they are taken into account. This is also consistent with the results of [41,43], since the parameter ξ that controls their mass spectrum is a simple function of K (3) . Furthermore, we also showed that in one particular case in which the matrix M is not invertible, we recover the residual flat direction found in [42] for the same flux choices.…”

Moduli stabilisation and the statistics of axion physics in the landscape

“…• The distribution of the string coupling g s is taken to be uniform. This result was explicitly checked in [5] for rigid CY manifolds and is believed to hold for more general cases as well [53]. Hence in the following we shall take dN dg s where N is the number of flux vacua.…”