Systematics of the α′ expansion in F-theory

Abstract

Extracting reliable low-energy information from string compactifications notoriously requires a detailed understanding of the UV sensitivity of the corresponding effective field theories. Despite past efforts in computing perturbative string corrections to the tree-level action, neither a systematic approach nor a unified framework has emerged yet. We make progress in this direction, focusing on the moduli dependence of perturbative corrections to the 4D scalar potential of type IIB Calabi-Yau orientifold compactifications. We proceed by employing two strategies. First, we use two rescaling symmetries of type IIB string theory to infer the dependence of any perturbative correction on both the dilaton and the Calabi-Yau volume. Second, we use F/M-theory duality to conclude that KK reductions on elliptically-fibred Calabi-Yau fourfolds of the M-theory action at any order in the derivative expansion can only generate (α′)even corrections to the 4D scalar potential, which, moreover, all vanish for trivial fibrations. We finally give evidence that (α′)odd effects arise from integrating out KK and winding modes on the elliptic fibration and argue that the leading no-scale breaking effects at string tree-level arise from (α′)3 effects, modulo potential logarithmic corrections.

LVS de Sitter Vacua are probably in the Swampland

“…We will not attempt to be complete but rather discuss a selection of corrections that are potentially relevant for our purpose. See also [15] for a recent survey of perturbative corrections in IIB/F-theory compactifications. It is well known that the Kähler potential in toroidal orientifold compactifications receives string-loop corrections at order α ′2 due to an exchange of Kaluza-Klein modes between D7/D3 branes or O7/O3 planes [29][30][31][32] (see also [33]).…”

“…The problem is rather that the 4D EFT describing this highly stringy regime is unknown and might look very different from the naive EFT derived from a dimensional reduction of 10D supergravity. 15 It follows from [28,66] that a necessary condition to avoid the singular-bulk problem is…”

“…Another source of higher F terms are 10D 8-derivative terms containing powers of the 3-form field strength G 3 . Dimensionally reducing such terms, one finds that they are suppressed by the same factor (3.20) compared to the ξ term in the LVS potential (2.5) [74] (see also [2,15,75]).…”

Quadratic curvature corrections to stringy effective actions and the absence of de Sitter vacua

“…For example, comparing terms O(α 3 g 2 s ) and O(α 2 g 3 s ) can be hard. A very important part of ongoing supergravity research is to systematically analyse these corrections at all orders and ensure that Kähler moduli stabilisation is not spoiled in the bulk of moduli space (see for example [11][12][13][14][15]). Furthermore, since we lack a complete picture of non-perturbative supergravity, it is difficult to define frameworks where computations can be carried out under complete control.…”

The LVS Parametric Tadpole Constraint

“…By comparison, the recent analysis of [20] used these conditions together with a number of conditions related to further corrections (see e.g. [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]) to collectively constrain the LVS. These analytical constraints were then applied to a specific Calabi-Yau orientifold.…”