Duality in Complex sine-Gordon Theory

New aspects of the complex sine-Gordon theory are addressed through the reformulation of the theory in terms of the gauged Wess-Zumino-Witten action. A dual transformation between the theory for the coupling constant \b > 0 and the theory for \b < 0 is given which agrees with the Krammers-Wannier duality in the context of perturbed conformal field theory. The B\"{a}cklund transform and the nonlinear superposition rule for the complex sine-Gordon theory are presented and from which, exact solutions, solitons and breathers with U(1) charge, are derived. We clarify topological and nontopological nature of neutral and charged solitons respectively, and discuss about the duality between the vector and the axial U(1) charges.Comment: 10 pages, LaTe

Solutions of Conformal Turbulence on a Half Plane

Exact solutions of conformal turbulence restricted on a upper half plane are obtained. We show that the inertial range of homogeneous and isotropic turbulence with constant enstrophy flux develops in a distant region from the boundary. Thus in the presence of an anisotropic boundary, these exact solutions of turbulence generalize Kolmogorov's solution consistently and differ from the Polyakov's bulk case which requires a fine tunning of coefficients. The simplest solution in our case is given by the minimal model of $p=2, q=33$ and moreover we find a fixed point of solutions when $p,q$ become large.Comment: 10pages, KHTP-93-07, SNUCTP-93-3