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New symmetries of supersymmetric effective Lagrangians
Phys. Rev. D 52, 1190 – Published 15 July, 1995
DOI: https://doi.org/10.1103/PhysRevD.52.1190
Abstract
We consider the structure of effective Lagrangians describing the low-energy dynamics of supersymmetric theories in which a global symmetry G is spontaneously broken to a subgroup H while supersymmetry is unbroken. In accordance with the supersymmetric Goldstone theorem, these Lagrangians contain Nambu-Goldstone superfields associated with a coset space /H^, where is the complexification of G and H^ is the largest subgroup of that leaves the order parameter invariant. The Lagrangian may also contain additional light matter fields. To analyze the effective Lagrangian for the matter fields we first consider the case where the effective Lagrangian is obtained by integrating out heavy modes at weak coupling (but including nonperturbative effects such as instantons). We show that the superpotential of the matter fields is H^ invariant, which can give rise to nontrivial relations among independent H invariants in the superpotential. We also show that the Kähler potential of the matter fields can be restricted by a remnant of H^ symmetry. These results are nonperturbative and have a simple group-theoretic interpretation. When we relax the weak-coupling constraints, there appear to be additional possibilities for the action of H^ on the matter fields, hinting that the constraints imposed by H^ may be even richer in strongly coupled theories.
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