Saddle point solutions in Yang-Mills-dilaton theory

The coupling of a dilaton to the $SU(2)$-Yang-Mills field leads to interesting non-perturbative static spherically symmetric solutions which are studied by mixed analitical and numerical methods. In the abelian sector of the theory there are finite-energy magnetic and electric monopole solutions which saturate the Bogomol'nyi bound. In the nonabelian sector there exist a countable family of globally regular solutions which are purely magnetic but have zero Yang-Mills magnetic charge. Their discrete spectrum of energies is bounded from above by the energy of the abelian magnetic monopole with unit magnetic charge. The stability analysis demonstrates that the solutions are saddle points of the energy functional with increasing number of unstable modes. The existence and instability of these solutions are "explained" by the Morse-theory argument recently proposed by Sudarsky and Wald.Comment: 11 page

Transonic flow on an axially symmetric torus

AbstractOn a Riemannian manifold the existence (and uniqueness) of subsonic gas flows with prescribed circulation has been previously established (Acta Math. 125 1970, 57–73). If the manifold is a torus of revolution then the gas dynamics equation reduces to a nonlinear ordinary differential equation and the flow can be described explicitly. We show that, as the circulations are increased, one obtains a complete family of solutions: smooth subsonic, smooth transonic, transonic with shocks, and smooth supersonic flows

Continuous families of H-surfaces

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