Finite field theories in three dimensions with and without supersymmetry
Necessary and sufficient conditions are derived for the finiteness of theS-matrix and vacuum stress of theories with Yukawa,ϕ3, andϕ4 couplings in three spacetime dimensions, and general supersymmetric solutions to these conditions are given. The requirement of a finiteS-matrix allows many non-supersymmetric solutions, but with two bosons and two fermions the additional constraint of a finite vacuum stress allows only one simple alternative to supersymmetry.
KeywordsField Theory Elementary Particle Quantum Field Theory Additional Constraint Particle Acceleration
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