Abstract
We consider 3d N=1 M-theory compactifications on Calabi-Yau fourfolds, and the effective 3d theory of light modes obtained by reduction from eleven dimensions. We study in detail the mass spectrum at the vacuum and, by decoupling the massive multiplets, we derive the effective 3d N=1 theory in the large-volume limit up to quartic fermion terms. We show that in general it is an ungauged N=1 supergravity of the form expected from 3d supersymmetry. In particular the massless bosonic fields consist of the volume modulus and the axions originating from the eleven-dimensional three-form, while the moduli-space metric is locally isometric to hyperbolic space. We consider the F-theory interpretation of the 3d N=1 M-theory vacua in the light of the F-theory effective action approach. We show that these vacua generally have F-theory duals with circle fluxes, thus breaking 4d Poincar\'e invariance.
Highlights
3d M-theory flux vacua with N = 2 supersymmetry from compactification on Calabi-Yau (CY) fourfolds were constructed in [3]
We consider 3d N = 1 M-theory compactifications on Calabi-Yau fourfolds, and the effective 3d theory of light modes obtained by reduction from eleven dimensions
We study in detail the mass spectrum at the vacuum and, by decoupling the massive multiplets, we derive the effective 3d N = 1 theory in the large-volume limit up to quartic fermion terms
Summary
The bosonic moduli are paired up with their fermionic superpartners, discussed in more detail, to form 3d massless N = 2 supergravity multiplets: gravity : gμν; χμ ; vector : AA, M A; λA ; scalar : Zα; λα , N I ; λI , where χμ is a complex gravitino and λA, λα, λI are complex 3d spinors. In our case the massive gravitino results from χ−μ eating the spinor field λ+ This can be seen by examining the quadratic fermion terms at the N = 1 Minkowski vacuum, cf (D.54), (D.63),. Taking (3.28), (C.14), (D.51) into account while setting to zero all massive fermions we obtain the following terms: 2ψM ΓMmR∇mψR d3x −g(3) 9∂μV (λ−γν γμχ′ν+) , (3.30). + GIJ(λI γμγν χ′μ+)∂ν N J + GUU ΓUIJ(λ−γμλI )∂μN J + GIJΓJUK (λI γμλ−)∂μN K + c.c. , which is precisely of the expected form of ungauged three-dimensional supergravity as given in [13, 14].9
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