Universal gauge theory

It is shown that there is a "universal" group that contains the gauge groups of all Yang-Mills theories as subgroups. An analogue of Yang-Mills theory ("universal gauge theory") with this group as the invariance group is shown to exist in 3+1 space-time dimensions. It has all the topological features of Yang-Mills theory, such as instantons and θ vacua, and is a renormalizable theory at the quantum level. The multi-instanton solutions of this theory are found explicitly. The constraint and the eigenvalue problem for the Hamiltonian are solved exactly for all values of θ. It is shown that at the quantum level universal gauge theory has the same spectrum as a (1+1)-dimensional free fermion system.