Publication : t86/189

Abstract:
The stability of the effective potential for two-dimensional membrane models with bending rigidity is studied in the limit d -> infinity; (where d is the dimension of space). For small enough surface tension, instabilities which break translation invariance in the plane of the membrane appear for large but finite wave-lengths. The possible connection between those instabilities, the branching transition in lattice random surface models and the existence of tachyons in string models are discussed. The formal relationship between membrane models in 25 dimensions and the 26-dimensional bosonic string model is outlined.