This thesis is a contribution to the search for new fundamental physics in the form of axionlike particles (ALPs). ALPs are relatively light and feebly interacting particles that are part of many theories extending the Standard Model of particle physics, e.g., to solve the strong-CP problem, the dark matter problem, or quantum gravity in the form of string theory. We use astrophysical observations mainly related to core-collapse supernovae to search for signatures of the existence of ALPs.

In the first part of this thesis, we study in some detail the effective field theory of ALPs with a focus on quantum loop effects. These loops necessarily induce correlations between the effective couplings of the theory such that, e.g., the interaction between ALPs and photons sourced by quantum loops due to their coupling to leptons cannot be neglected. In the second part of the thesis, as well as in three of the publications that it is comprised of, we demonstrate the importance of the effective ALP-photon coupling defined here for dark matter ALPs, whose loop induced decay to photons excludes a large region of their parameter space that was believed to be accessible to direct detection experiments, as well as ALPs produced in supernova explosions. Through the loop-induced interaction with photons more ALPs can be produced in supernovae than was calculated previously. Additionally, the photon-decay channel implies ways in which ALPs could have been observed that would not be possible if they only interacted with leptons. For instance, if a nearby supernova such as SN 1987A or the recently observed SN 2023ixf, emitted a large number of ALPs that afterwards decayed into gamma-ray photons, such a signal could have been detected by telescopes. The precise prediction of this signal is a further focus of this thesis and three of the included publications. Additionally, we improve many technical aspects of the determination of the number and energy of ALPs produced in supernovae, as well as their reabsorption before they can leave the hot and dense inner regions. This enables us to derive some of the strongest, and most reliable bounds to date on the parameters of ALPs.