The Hoyle state in Nuclear Lattice EFT

We review the calculation of the Hoyle state of ${}^{12}$C in Nuclear Lattice Effective Field Theory (NLEFT) and its anthropic implications for the nucleosynthesis of ${}^{12}$C and ${}^{16}$O in red giant stars. We also review the extension of NLEFT to the regime of medium-mass nuclei, with emphasis on the determination of the ground-state energies of the alpha nuclei ${}^{16}$O, ${}^{20}$Ne, ${}^{24}$Mg and ${}^{28}$Si by means of Euclidean time projection. Finally, we review recent NLEFT results for the spectrum, electromagnetic properties, and alpha-cluster structure of ${}^{16}$O.