Anomalous dimensions of high-gradient operators in then-vector model in 2+? dimensions

Abstract

The anomalous dimensions of operators with an arbitrary number of gradients are determined for then-vector model ind=2+e dimensions in one-loop order. For those operators which do not vanish ind=2 dimensions all anomalous dimensions can be given explicitly. Among the scalar operators (underO(n) andO(d)) with 2s derivatives there is an operator with the full dimensiony=2(1−s)+ɛ(1+s(s−1)/(n−2))+O(ɛ2). Thus similarly as for theQ-matrix model investigated by Kravtsov, Lerner, and Yudson, large positive corrections in one-loop order are obtained for then-vector model. Possible consequences of the corrections are discussed.