  Mounting evidence suggests that Luminous Fast Blue Optical Transients
(LFBOTs) are powered by a compact object, launching an asymmetric and fast
outflow responsible for the radiation observed in the ultraviolet, optical,
infrared, radio, and X-ray bands. Proposed scenarios aiming to explain the
electromagnetic emission include an inflated cocoon, surrounding a jet choked
in the extended stellar envelope. In alternative, the observed radiation may
arise from the disk formed by the delayed merger of a black hole with a
Wolf-Rayet star. We explore the neutrino production in these scenarios, i.e.
internal shocks in a choked jet and interaction between the outflow and the
circumstellar medium (CSM). If observed on-axis, the choked jet provides the
dominant contribution to the neutrino fluence. Intriguingly, the IceCube upper
limit on the neutrino emission inferred from the closest LFBOT, AT2018cow,
excludes a region of the parameter space otherwise allowed by electromagnetic
observations. After correcting for the Eddington bias on the observation of
cosmic neutrinos, we conclude that the emission from an on-axis choked jet and
CSM interaction is compatible with the detection of two track-like neutrino
events observed by the IceCube Neutrino Observatory in coincidence with
AT2018cow, and otherwise considered to be of atmospheric origin. While the
neutrino emission from LFBOTs does not constitute the bulk of the diffuse
background of neutrinos observed by IceCube, detection prospects of nearby
LFBOTs with IceCube and the upcoming IceCube-Gen2 are encouraging. Follow-up
neutrino searches will be crucial for unravelling the mechanism powering this
emergent transient class.
