New symmetries of supersymmetric effective Lagrangians.

摘要

We consider the structure of effective lagrangians describing the low-energydynamics of supersymmetric theories in which a global symmetry $G$ isspontaneously broken to a subgroup $H$ while supersymmetry is unbroken. Inaccordance with the supersymmetric Goldstone theorem, these lagrangians containNambu--Goldstone superfields associated with a coset space $G^c / \hat{H}$,where $G^c$ is the complexification of $G$ and $\hat{H}$ is the largestsubgroup of $G^c$ that leaves the order parameter invariant. The lagrangian mayalso contain additional light matter fields. To analyze the effectivelagrangian for the matter fields, we first consider the case where theeffective lagrangian is obtained by integrating out heavy modes at weakcoupling (but including non-perturbative effects such as instantons). We showthat the superpotential of the matter fields is $\hat{H}$ invariant, which cangive rise to non-trivial relations among independent $H$-invariants in thesuperpotential. We also show that the Kahler potential of the matter fields canbe restricted by a remnant of $\hat{H}$ symmetry. These results arenon-perturbative and have a simple group-theoretic interpretation. When werelax the weak-coupling constraint, there appear to be additional possibilitiesfor the action of $\hat{H}$ on the matter fields, hinting that the constraintsimposed by $\hat{H}$ may be even richer in strongly coupled theories.