FANCY AND FACTS IN THE (d - 2) EXPANSION OF NON-LINEAR SIGMA MODELS
نویسنده
چکیده
We review the existing results on the scaling dimensions of operators with more than two derivatives in the non-linear sigma models. We argue that the speculations on the relevance of these operators, and correspondingly on the breakdown of the (d−2) expansion for the classical Heisenberg model, or for the one-parameter scaling theory of localization, are based on a dubious mathematical analysis. The low temperature expansion of the N -vector model is given by a model of interacting Goldstone bosons, known as the non-linear sigma model [1, 2]. The existence of a zero-temperature fixed point in dimension two has led to an expansion of the critical properties in powers of (d−2) which supplements the familiar expansion in powers of (4−d) based on the linear Landau-GinzburgWilson model [3]; linear and non-linear refer here to the representation of the O(N) symmetry by the order parameter. These non-linear sigma models were generalized to situations in which the order parameter is a mapping of a two-dimensional lattice onto a target manifold (a sphere in the case of the O(N) model). These generalizations are the basis of the conformal field theory approach to string theory, and they 1 Unité propre du Centre National de la Recherche Scientifique, associée à l’Ecole Normale Supérieure et à l’Université de Paris-Sud
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تاریخ انتشار 1996