Effective action from M-theory on twisted connected sum $G_2$-manifolds

Understand

We study the four-dimensional low energy effective $\mathcal{N}=1$ supergravity theory of the dimensional reduction of M-theory on $G_2$-manifolds, which are constructed by Kovalev's twisted connected sum gluing suitable pairs of asymptotically cylindrical Calabi-Yau threefolds $X_{L/R}$ augmented with a circle $S^1$.

• In the Kovalev limit the Ricci-flat $G_2$-metrics are approximated by the Ricci-flat metrics on $X_{L/R}$ and we identify the universal modulus - the Kovalevton - that parametrizes this limit.
• We observe that the low energy effective theory exhibits in this limit gauge theory sectors with extended supersymmetry.
• We determine the universal (semi-classical) K\"ahler potential of the effective $\mathcal{N}=1$ supergravity action as a function of the Kovalevton and the volume modulus of the $G_2$-manifold.