The effective action of warped M-theory reductions with higher-derivative terms. Part II

Abstract

Abstract:We study the three-dimensional effective action obtained by reducing elevendimensional supergravity with higher-derivative terms on a background solution including a warp-factor, an eight-dimensional compact manifold, and fluxes. The dynamical fields are Kähler deformations and vectors from the M-theory three-form. We show that the potential is only induced by fluxes and the naive contributions obtained from higher-curvature terms on a Calabi-Yau background vanish once the back-reaction to the full solution is taken into account. For the resulting three-dimensional action we analyse the Kähler potential and complex coordinates and show compatibility with N = 2 supersymmetry. We argue that the higher-order result is also compatible with a no-scale condition. We find that the complex coordinates should be formulated as divisor integrals for which a non-trivial interplay between the warp-factor terms and the higher-curvature terms allow a derivation of the moduli space metric. This leads us to discuss higher-derivative corrections to the M5-brane action.

Weakly coupled de Sitter vacua with fluxes and the swampland

“…9 In the presence of localized sources such as O-planes or D-branes, compactifications are typically warped. While the resulting subtleties in the 4d effective field theory are relatively well understood in type IIB/F-theory (see, e.g., [124][125][126][127][128][129][130][131][132][133][134][135][136][137] and references therein), not much about this issue is known in type IIA. In the following, we ignore warping and assume that the 4d scalar potential is wellapproximated by (3.1).…”

α′-Corrections and de Sitter vacua - A mirage?

“…the powers of α cancel. In other words the additional conditions (19) can be satisfied by tuning |W 0 | according to (21) if (20) exhibits a solution for v i 0 . One infers the volume in the extremum to be…”

On four-derivative terms in IIB Calabi-Yau orientifold reductions

“…However, a complete discussion of the reduction results of the R 4 -sector on a Calabi-Yau threefold involves a proper treatment of the ten-dimensional background solution at this order, with a successive dimensional reduction on this modified background. The analog scenario of the R 4 -sector in a dimensional reduction on a CalabiYau fourfold with Kähler deformations was discussed in the context of M-theory/F-theory in [34][35][36][37][38], where a complete treatment involving the corrected background was provided. Furthermore, the dimensional reduction of the R 4 -sector was discussed in related set-ups in [39,40].…”

“…However, a more refined analysis would be required to fully justify this choice. See [38,46] for a more detailed discussion of the problem. 2 Combining the uplift of the reduction result (2.13), (2.15) and the terms, which arose due to Weyl rescaling (A.16) and (A.17), and by using the definition G µν := R µν − 1 4 g µν R, which is defined in close analogy to the Einstein tensor 3 one finds…”