Effective lagrangians for four-dimensional superstrings

Abstract

We derive effective supergravity lagrangians for the massless sector of new four-dimensional superstrings. The untwisted sector is obtained by suitable Z 2 or Z 2 ⊗ Z 2 ′ truncations of N = 4, D = 4 lagrangians. For the N = 1 “minimal” models, related to the N = 4, SO(44) superstrings, we derive the Kähler potential, the superpotential and the ƒ gauge kinetic function. The underlying nonlinear sigma model is based on the Kähler manifold [SU(1,1)/U(1)] ⊗ Π i = 1 3 {SO(2, n i )/[SO(2) ⊗ SO( n i )]}. For models without massless twisted sector, this result provides the full superstring low-energy effective action. For models with massless twisted sector, the N = 1 theory may be obtained once the quaternionic manifold of the corresponding N = 2 hypermultiplets is specified.