3d N = 1 $$ \mathcal{N}=1 $$ effective supergravity and F-theory from M-theory on fourfolds

We investigate M-theory and heterotic compactifications to 7 and 3 dimensions. In 7 dimensions we discuss a class of massive supergravities that arise from M-theory on K3 and point out obstructions to realizing these theories in a dual heterotic framework with a geometric description. Taking M-theory further down to 3 dimensions on K3 × K3 with a choice of flux leads to a rich landscape of theories with various amounts of supersymmetry, including those preserving 6 supercharges. We explore possible heterotic realizations of these vacua and prove a no-go theorem: every heterotic geometry that preserves 6 supercharges preserves 8 supercharges.

Section: Massless Spectrummentioning

confidence: 99%

Non-duality in three dimensions

Melnikov

Minasian

Sethi

2017

“…In this paper we will not consider fluxes but focus on the geometric constructions. Of course it is interesting to consider this in the future and study the effects of these on supersymmetry breaking and potential obstructions to dualities, both M/F-duality [34], where in particular 4d Poincaré invariance could be broken, as well as obstructions to M-theory/weakly-coupled heterotic duality [35,36].…”

Section: Jhep06(2018)103mentioning

confidence: 99%

Spin(7)-manifolds as generalized connected sums and 3d $$ \mathcal{N}=1 $$ theories

Braun¹,

Schäfer‐Nameki²

2018

M-theory on compact eight-manifolds with Spin(7)-holonomy is a framework for geometric engineering of 3d N = 1 gauge theories coupled to gravity. We propose a new construction of such Spin(7)-manifolds, based on a generalized connected sum, where the building blocks are a Calabi-Yau four-fold and a G 2 -holonomy manifold times a circle, respectively, which both asymptote to a Calabi-Yau three-fold times a cylinder. The generalized connected sum construction is first exemplified for Joyce orbifolds, and is then used to construct examples of new compact manifolds with Spin(7)-holonomy. In instances when there is a K3-fibration of the Spin(7)-manifold, we test the spectra using duality to heterotic on a T 3 -fibered G 2 -holonomy manifold, which are shown to be precisely the recently discovered twisted-connected sum constructions.

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

Grimm

Pugh

Weissenbacher

2015

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.