Non-supersymmetric F-theory compactifications on Spin(7) manifolds

Abstract

We propose a novel approach to obtain four-dimensional effective actions coupled to supersymmetry-breaking boundaries by considering F-theory on manifolds with special holonomy Spin(7). To perform such studies we suggest that a duality relating Mtheory on a certain class of Spin(7) manifolds with F-theory on the same manifolds times an interval exists. The Spin(7) geometries under consideration are constructed as quotients of elliptically fibered Calabi-Yau fourfolds by an anti-holomorphic and isometric involution. The three-dimensional minimally supersymmetric effective action of M-theory on a general Spin(7) manifold with fluxes is determined and specialized to the aforementioned geometries. This effective theory is compared with an interval Kaluza-Klein reduction of a non-supersymmetric four-dimensional theory with definite boundary conditions for all fields. Using this strategy a minimal set of couplings of the four-dimensional low-energy effective actions is obtained in terms of the Spin(7) geometric data. We also discuss briefly the string interpretation in the Type IIB weak coupling limit.

Singular foliations for M-theory compactification

“…the class of backgrounds discussed here appears to be connected with the proposals of [6] and [7], connections which deserve to be explored in detail.…”

“…They form a useful testing ground for various proposals aimed at providing unified descriptions of flux backgrounds [6] and may be relevant to recent attempts to gain a better understanding of F-theory [7]. When the internal part ξ of the supersymmetry generator is everywhere non-chiral, such backgrounds can be studied [8] using foliations endowed with longitudinal G 2 structures, an approach which permits a geometric description of the supersymmetry conditions while providing powerful tools for studying the topology of such backgrounds.…”

“…Since L is connected and maximal with this property, the graph E L obtained fromÊ L by identifying to a single point the vertices of each of the subsetsŝ 1 (L ′′ α ) is a connected component of E. It follows that the strong singular leaves ofF ω are in one to one correspondence with the connected components of the graph E -namely, their subgraphsÊ L are the preimages through p of those components. 7 If s1(L) is empty, this operation does nothing. Figure 2.…”

“…Reference [1] uses a one-form ω 1 ∈ Ω 1 (M ) and a three-form ω 2 ∈ Ω 3 (M ) which are given by [1, eq. (3.18)]: [7] , (C.12) [7] − 6 7 ι ιLF [7] Φ + 1 4 ι L F [27] .…”

“…E Some topological properties of singular foliations defined by a Morse one-form 55 E.1 Some topological invariants of M 55 E.2 Estimate for the number of splitting saddle points 55 E. 3 Estimates for c and N min 56 E. 4 Criteria for existence and number of homologically independent compact leaves 56 E.5 Generic forms 56 E.6 Exact forms 57 E. 7 Behavior under exact perturbations 57 1 Introduction N = 1 flux compactifications of eleven-dimensional supergravity on eight-manifolds M down to AdS 3 spaces [1,2] provide a vast extension of the better studied class of compactifications down to 3-dimensional Minkowski space [3][4][5], having the advantage that they are already consistent at the classical level [2]. They form a useful testing ground for various proposals aimed at providing unified descriptions of flux backgrounds [6] and may be relevant to recent attempts to gain a better understanding of F-theory [7].…”