Bounds on the coupling of the Majoron to light neutrinos from supernova cooling

We explore the role of Majoron (J) emission in the supernova cooling process, as a source of the upper bound on neutrino-Majoron coupling. We show that the strongest upper bound on the coupling to nu(e) comes from the nu(e)nu(e)-->J process in the core of a supernova. We also find bounds on diagonal couplings of the Majoron to nu(mu(tau))nu(mu(tau)) and on off-diagonal nu(e)nu(mu(tau)) couplings in various regions of the parameter space. We discuss the evaluation of the cross section for four-particle interactions (nunu-->JJ and nuJ-->nuJ). We show that these are typically dominated by three-particle subprocesses and do not give new independent constraints.