The critical O(N) CFT: Methods and conformal data

TL;DR

This paper reviews the critical $O(N)$ conformal field theory in dimensions between 2 and 4, highlighting methods and providing extensive conformal data, including new computations of anomalous dimensions.

Contribution

It offers a comprehensive overview of the $O(N)$ CFT, compiling existing data and adding new $ ext{O}(oldsymbol{ ext{ε}})$ anomalous dimensions, serving as a valuable resource for researchers.

Findings

Extensive conformal data for the $O(N)$ CFT across various dimensions.

New computations of anomalous dimensions at order ε.

Compilation of methods and results from literature.

Abstract

The critical $O(N)$ CFT in spacetime dimensions $2 < d < 4$ is one of the most important examples of a conformal field theory, with the Ising CFT at $N=1$, $2 \leq d < 4$, as a notable special case. Apart from numerous physical applications, it serves frequently as a concrete testing ground for new approaches and techniques based on conformal symmetry. In the perturbative limits - the $4-\varepsilon$ expansion, the large $N$ expansion and the $2+\tilde\epsilon$ expansion - a lot of conformal data have been computed over the years. In this report, we give an overview of the critical $O(N)$ CFT, including some methods to study it, and present a large collection of conformal data. The data, extracted from the literature and supplemented by many additional computations of order $\varepsilon$ anomalous dimensions, are made available through an ancillary data file.