Spontaneous generation of massive multiplets and central charges in extended supersymmetric theories

Abstract

Massless gauge theories invariant under extended supersymmetry algebras with N = 2 or N = 4 spinorial generators have U(2) or SU(4) as the global internal symmetry group. The translation of scalar fields in these theories generate massive, gauge or matter, multiplets of various types. The existence of most of these multiplets requires an (apparent) modification of the structure of the algebra: in the anticommutators of spinorial generators we now find “central charges”, which commute with all symmetries of the theory. Such central charges are not new symmetries, but only some of the (Abelian or non-Abelian) generators of the gauge group, which are preserved by the translation. In the non-Abelian case, the promotion of some of the Yang-Mills generators to the role of central charges implies of course a spontaneous breaking of the Yang-Mills group. In addition the appearance of central charges in the algebra requires a breaking of the global internal symmetry group U(2) or SU(4) to a smaller subgroup. The generation of masses in an originally massless theory results in a massless gauge or matter multiplet containing the following noteworthy fields: the dilaton, one or several Goldstone bosons, and N pseudo-Goldstone spinors, associated with the breaking of dilatation, global internal symmetry and the N extra spinorial generators appearing in the conformal superalgebra (while the N ordinary supersymmetry generators remain conserved). The connection between the dilaton and central charges leads to a relation between the (mass) 2 operator and the sum of the squares of the central charges (and to the possibility of mass quantization). This can be interpreted by comparing the central charges with the translation operators in a two- or six-dimensional compact internal symmetry space.