Three-dimensional Yang-Mills-Higgs equations in gauge-invariant variables

A formulation of three-dimensionalSU(2) andSO(1,2) Yang-Mills theories in the gauge-invariant variablesG _ij=tr^* F _i ^* F_j is proposed. It is shown that the tensorG _ij satisfies three-dimensional Einstein equations with simple right-hand side andG _ij playing the role of a metric. This result is generalized to the case of a system of Yang-Mills-Higgs fields.Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 94, No. 1, pp. 66–75, January, 1993.