The minimal conformal O(N) vector sigma model at d=3

TL;DR

This paper analyzes the minimal O(N) sigma model in three dimensions, showing that all n-point functions up to order 1/N are expressible by elementary functions, revealing simple conformal dimensions of composite fields.

Contribution

It provides an explicit, elementary-function-based description of n-point functions and conformal dimensions in the minimal O(N) sigma model at order 1/N.

Findings

All n-point functions up to order 1/N are elementary functions.

Conformal dimensions of composite fields are proportional to the number of auxiliary fields.

The model exhibits simplified structure without logarithmic complexities.

Abstract

For the minimal O(N) sigma model, which is defined to be generated by the O(N) scalar auxiliary field alone, all n-point functions, till order 1/N included, can be expressed by elementary functions without logarithms. Consequently, the conformal composite fields of m auxiliary fields possess at the same order such dimensions, which are m times the dimension of the auxiliary field plus the order of differentiation.