On O(N_c) d=3 N=2 supersymmetric QCD Theories

We study three dimensional N=2 supersymmetric QCD theories with O(N_c) gauge groups and with N_f chiral multiplets in the vector representation. We argue that for N_f < N_c-2 there is a runaway potential on the moduli space and no vacuum. For N_f >= N_c-2 there is a moduli space also in the quantum theory, and for N_f >= N_c-1 there is a superconformal fixed point at the origin of this moduli space that has a dual description as the low-energy fixed point of an O(N_f-N_c+2) gauge theory. We test this duality in various ways; in some cases the duality for an O(2) gauge theory may be related to the known duality for U(1) gauge theories. We also discuss real mass deformations, which allow to connect theories with a different Chern-Simons level. This allows us to connect our duality with the known duality in O(N_c) theories with a Chern-Simons term of level k, where the dual gauge group is given by O(N_f+|k|-N_c+2).Comment: 28 pages. v2: minor changes, added reference

Globalization of the actions of the Lie symmetries of nonlinear wave equations with dissipation

The classification of the Lie point symmetries of the nonlinear wave equations with dissipation give a generic case and eight special cases. In this article we show that in seven of the eight cases the action of the Lie symmetries can be globalized via induced representations of a family of solvable Lie groups. In one special case, we show that the action of the Lie symmetries can be globalized by using an induced representation of (Formula presented.)