Consequences of the complex character of the internal symmetry in supersymmetric theories
The consequences of the invariance of the superpotential under the complexification \(G^ c\) of the internal symmetry group on the determination of the possible patterns of symmetry and supersymmetry breaking are established in a globally supersymmetric theory. In particular, in the case of global internal symmetry we show that the vacuum associated to a point z, where \(G_ z^ c\neq G^ c_ z\) is always degenerate with a vacuum associated to a point z', where \(G^ c_{z'}=G_{z'}^ c\); all the other degeneracies of the minimum of the potential on an orbit of \(G^ c\) are also determined and shown to be completely removed when the internal symmetry is gauged. The zeroes of the D-term of a supersymmetric gauge theory are characterized as the points of the closed orbits of \(G^ c\) which are at minimum distance from the origin; at these points \(G^ c_ z=G_ z^ c\). It is rigorously proved that the minimum of the potential is zero if the gradient of the superpotential vanishes somewhere. It is also shown that the D-term necessarily vanishes at the minimum of the potential if the direction of spontaneous supersymmetry breaking is invariant by G.
scientific article; zbMATH DE number 3979974