The Hoyle state in nuclear lattice effective field theory

We review the calculation of the Hoyle state of ¹²C in nuclear lattice effective field theory (NLEFT) and its anthropic implications in the nucleosynthesis of ¹²C and ¹⁶O in red giant stars. We also analyse the extension of NLEFT to the regime of medium-mass nuclei, with emphasis on the determination of the ground-state energies of the α nuclei ¹⁶O, ²⁰Ne, ²⁴Mg, and ²⁸Si by Euclidean time projection. Finally, we discuss recent NLEFT results for the spectrum, electromagnetic properties, and α-cluster structure of ¹⁶O.