  Active matter is not only relevant to living matter and diverse
nonequilibrium systems, but also constitutes a fertile ground for novel
physics. Indeed, dynamic renormalization group (DRG) analyses have uncovered
many new universality classes (UCs) in polar active fluids - an archetype of
active matter systems. However, due to the inherent technical difficulties in
the DRG methodology, almost all previous studies have been restricted to polar
active fluids in the incompressible or infinitely compressible (i.e.,
Malthusian) limits, and, when the $\epsilon$-expansion was used in conjunction,
to the one-loop level. Here, we use functional renormalization group methods to
bypass some of these difficulties and unveil for the first time novel critical
behavior in compressible polar active fluids, and calculate the corresponding
critical exponents beyond the one-loop level. Specifically, focusing on a
multicritical region of the system, we find three novel UCs and quantify their
associate scaling behavior near the upper critical dimension $d_c = 6$.
