Classical and Quantum Integrability of 2D Dilaton Gravities in Euclidean space

Euclidean dilaton gravity in two dimensions is studied exploiting its representation as a complexified first order gravity model. All local classical solutions are obtained. A global discussion reveals that for a given model only a restricted class of topologies is consistent with the metric and the dilaton. A particular case of string motivated Liouville gravity is studied in detail. Path integral quantisation in generic Euclidean dilaton gravity is performed non-perturbatively by analogy to the Minkowskian case.Comment: 27 p., LaTeX, v2: included new refs. and a footnot

Monopole Vacuum in Non-Abelian Theories

It is shown that, in the theory of interacting Yang -Mills fields and a Higgs field, there is a topological degeneracy of Bogomol'nyi-Prasad-Sommerfield (BPS) monopoles and that there arises, in this case, a chromoelectric monopole characterized by a new topological variable that describes transitions between topological states of the monopole in the Minkowski space (in just the same way as an instanton describes such transitions in the Euclidean space). The limit of an infinitely large mass of the Higgs field at a finite density of the BPS monopole is considered as a model of the stable vacuum in the pure Yang-Mills theory. It is shown that, in QCD, such a monopole vacuum may lead to a rising potential, a topological confinement and an additional mass of the $\eta_0$ meson. The relationship between the result obtained here for the generating functional of perturbation theory and Faddeev-Popov integral is discussed