From M-theory higher curvature terms to α ′ corrections in F-theory

Abstract

We perform a Kaluza-Klein reduction of eleven-dimensional supergravity on a Calabi-Yau fourfold including terms quartic and cubic in the Riemann curvature and determine the induced corrections to the three-dimensional N = 2 effective action. We focus on the effective Einstein-Hilbert term and the kinetic terms for vectors. Dualizing the vectors into scalars, we derive the resulting Kähler potential and complex coordinates. The classical expressions for the Kähler coordinates are non-trivially modified, while the functional form of the Kähler potential is shown to be uncorrected. For elliptically fibered Calabi-Yau fourfolds the corrections can be uplifted to a four-dimensional F-theory compactification. We argue that also the four-dimensional N = 1 Kähler coordinates receive non-trivial corrections. We find a simple expression for the induced corrections for different Abelian and non-Abelian seven-brane configurations by scanning over many Calabi-Yau fourfolds with resolved singularities. The interpretation of this expression leads us to conjecture that the higher-curvature corrections correspond to α ′2 corrections that arise from open strings at the selfintersection of seven-branes.

The Swampland: Introduction and Review

“…It therefore remains an open problem to show that these terms are absent in general. However, no such dangerous leading terms have been found in string theory so far, despite extensive attempts to understand them quantitatively, see for example []. It therefore may be that such leading terms are forbidden, or sufficiently suppressed, in string theory due to some as yet unknown reason, or simply that they have not been calculated due to the technical difficulty of the problem.…”

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

“…It is obtained from the parent N = 2 theory arising from compactification of type IIB on Calabi-Yau orientifolds [4,5]. Secondly, evidence has been provided for the existence of a α 2 -correction to the Kähler coordinates utilizing F-theory based on a series of papers [6][7][8][20][21][22]. This formulation of Type IIB string theory with space-time filling seven-branes at varying string coupling [23] captures the string coupling dependence in the geometry of an elliptically fibered Calabi-Yau fourfold with base B 3 .…”

“…It is thus of great interest to advance beyond the classical results [3]. In this work we analyze the role of the leading order α -corrections to the fourdimensional, N = 1 effective actions of type IIB orientifold compactifications [4][5][6][7][8][9][10] in Kähler moduli stabilization [8,9,11]. We argue that due to the presence of the α -corrections Minkowski and de Sitter vacua may be obtained for Calabi-Yau orientifolds of positive Eulercharacteristic.…”

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].…”