Yang-Mills instantons and dyons on group manifolds

We consider Euclidean SU(N) Yang-Mills theory on the space G x R, where G is a compact semisimple Lie group, and introduce first-order BPS-type equations which imply the full Yang-Mills equations. For gauge fields invariant under the adjoint G-action these BPS equations reduce to first-order matrix equations, to which we give instanton solutions. In the case of G = SU(2) congruent to S-3. our matrix equations are recast as Nahm equations, and a further algebraic reduction to the Toda chain equations is presented and solved for the SU(3) example. Finally, we change the metric on G x R to Minkowski and construct finite-energy dyon-type Yang-Mills solutions. The special case of G = SU(2) x SU(2) may be used in heterotic flux compactifications. (C) 2008 Elsevier B.V. All rights reserved.