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.