Abstract
We study the three-dimensional effective action obtained by reducing eleven-dimensional 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 \( \mathcal{N}=2 \) 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.
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Grimm, T.W., Pugh, T.G. & Weissenbacher, M. The effective action of warped M-theory reductions with higher-derivative terms. Part II. J. High Energ. Phys. 2015, 1–25 (2015). https://doi.org/10.1007/JHEP12(2015)117
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DOI: https://doi.org/10.1007/JHEP12(2015)117