NEW SYMMETRIES OF SUPERSYMMETRIC EFFECTIVE LAGRANGIANS

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 unbro ken. In accordance with the supersymmetric Goldstone theorem, these La grangians contain Nambu-Goldstone superfields associated with a coset space G(c)/($) over cap H, where G(c) is the complexification of G and ($) over cap H is the largest subgroup of G(c) that leaves the order parameter invariant. The Lagrangian may also contain additional light matter fields. To analyze the effective Lagrangian for the matter fiel ds we first consider the case where the effective Lagrangian is obtain ed by integrating out heavy modes at weak coupling (but including nonp erturbative effects such as instantons). We show that the superpotenti al of the matter fields is H invariant, which can give rise to nontriv ial relations among independent H invariants in the superpotential. We also show that the Kahler potential of the matter fields can be restr icted by a remnant of ($) over cap H symmetry. These results are nonpe rturbative and have a simple group-theoretic interpretation. When we r elax the weak-coupling constraint, there appear to be additional possi bilities for the action of a on the matter fields, hinting that the co nstraints imposed by ($) over cap H may be even richer in strongly cou pled theories.