Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-12-24
Int.J.Mod.Phys. A14 (1999) 2551-2580
Physics
High Energy Physics
High Energy Physics - Theory
25 pages, LaTeX
Scientific paper
10.1142/S0217751X99001275
We discuss certain integrable quantum field theories in (1+1)-dimensions consisting of coupled sine/sinh-Gordon theories with N=1 supersymmetry, positive kinetic energy, and bosonic potentials which are bounded from below. We show that theories of this type can be constructed as Toda models based on the exceptional affine Lie superalgebra $D(2,1;\A)^{(1)}$ (or on related algebras which can be obtained as various limits) provided one adopts appropriate reality conditions for the fields. In particular, there is a continuous family of such models in which the couplings and mass ratios all depend on the parameter $\A$. The structure of these models is analyzed in some detail at the classical level, including the construction of conserved currents with spins up to 4. We then show that these currents generalize to the quantum theory, thus demonstrating quantum-integrability of the models.
Evans Jonathan M.
Madsen Jens Ole
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