  At least two multi-planetary systems in a 4:3 mean motion resonance have been
found by radial velocity surveys. These planets are gas giants and the systems
are only stable when protected by a resonance. Additionally the Kepler mission
has detected at least 4 strong candidate planetary systems with a period ratio
close to 4:3.
  This paper investigates traditional dynamical scenarios for the formation of
these systems. We systematically study migration scenarios with both N-body and
hydro-dynamic simulations. We investigate scenarios involving the in-situ
formation of two planets in resonance. We look at the results from finely tuned
planet-planet scattering simulations with gas disk damping. Finally, we
investigate a formation scenario involving isolation-mass embryos.
  Although the combined planet-planet scattering and damping scenario seems
promising, none of the above scenarios is successful in forming enough systems
in 4:3 resonance with planetary masses similar to the observed ones. This is a
negative result but it has important implications for planet formation.
Previous studies were successful in forming 2:1 and 3:2 resonances. This is
generally believed to be evidence of planet migration. We highlight the main
differences between those studies and our failure in forming a 4:3 resonance.
We also speculate on more exotic and complicated ideas. These results will
guide future investigators toward exploring the above scenarios and alternative
mechanisms in a more general framework.
