RIGID STRINGS FROM FIELD-THEORY

We study two simple phi-4 models in 2 + 1 dimensions which both have string-like classical solutions. They differ in that one has a conventional second-order kinetic term, while the other also has a beta-phi Square 2-phi term. We show that the strings in the first model is of Nambu-Goto type, while the strings in the latter are rigid, with a rigidity parameter approximately 1/beta. We show that if the fourth-order term arises by integrating out heavy fields from a realistic QFT, the rigidity term becomes negative, and the corresponding strings are not smooth. We also discuss the relevance of these results for more realistic models.