Boundedness from below of SU(n) potentials Sousa Da Fonseca, Renato Miguel I acknowledge the financial support from MCIN/AEI (10.13039/501100011033) through Grant No. PID2019– 106087GB-C22, from the Junta de Andalucía through Grant No. P18-FR-4314 (FEDER), from the Grant Agency of the Czech Republic (GAČR) through Contract No. 20-17490S, and also from the Charles University Research Center UNCE/SCI/013. Vacuum stability requires that the scalar potential is bounded from below. Whether or not this is true depends only on the scalar quartic interactions, but even so the analysis is arduous and has only been carried out for a limited set of models. Complementing the existing literature, this work contains the necessary and sufficient conditions for two SU(n) invariant potentials to be bounded from below. In particular, expressions are given for models with the fundamental and the 2-index (anti)symmetric representations of this group. A sufficient condition for vacuum stability is also provided for models with the fundamental and the adjoint representations. Finally, some considerations are made concerning the model with the gauge group SU(2) and the scalar representations 1, 2, and 3; such a setup is particularly important for neutrino mass generation and lepton number violation. 2022-05-11T07:13:33Z 2022-05-11T07:13:33Z 2022-04-14 journal article Renato M. Fonseca. Boundedness from below of SU(n) potentials. Phys. Rev. D 105, 075014 [DOI: 10.1103/PhysRevD.105.075014] http://hdl.handle.net/10481/74791 10.1103/PhysRevD.105.075014 eng http://creativecommons.org/licenses/by/3.0/es/ open access Atribución 3.0 España American Physical Society