  New light particles produced in supernovae can lead to additional energy loss
and a consequent deficit in neutrino production in conflict with the neutrinos
observed from Supernova 1987A (SN1987A). Contrary to the majority of previous
SN1987A studies, we examine the impact of $Z'$ bosons, axions, and axion-like
particles (ALPs) interacting with the muons produced in SN1987A. For the first
time, we find constraints on generic $Z'$ bosons coupled to muons, and apply
our results to particle models including gauged $L_\mu-L_\tau$ number,
$U(1)_{L_\mu-L_\tau}$, and gauged $B-L$ number, $U(1)_{B-L}$. We constrain $Z'$
bosons with masses up to about 250-500 MeV, and down to about $10^{-9}$ in
$Z'$-muon coupling. We also extend previous work on axion-muon couplings by
examining the importance of loop-level interactions, as well as performing
calculations over a wider range of axion masses. We constrain muon-coupled
axions from arbitrarily low masses up to about 200-500 MeV, with bounds
extending down to axion-muon couplings of approximately $10^{-8}$ GeV$^{-1}$.
We conclude that supernovae broadly provide a sensitive probe of new
lightly-coupled particles interacting with muons.
