Irreversibility and higher-spin conformal field theory

TL;DR

This paper explores higher-spin conformal field theories, analyzing their central charges, operator structures, and quantum properties, revealing non-unitarity but interesting features like positive central charges and potential fixed points.

Contribution

It provides the first detailed calculation of central charges for higher-spin conformal theories and examines their operator-product structures and quantum behavior.

Findings

Higher-spin conformal tensors have positive-definite actions and gauge invariance.

Higher-spin conformal spinors can be coupled to gauge fields and contribute to beta functions.

Some theories violate the Ferrara-Gatto-Grillo theorem, indicating novel operator properties.

Abstract

I discuss the properties of the central charges c and a for higher-derivative and higher-spin theories (spin 2 included). Ordinary gravity does not admit a straightforward identification of c and a in the trace anomaly, because it is not conformal. On the other hand, higher-derivative theories can be conformal, but have negative c and a. A third possibility is to consider higher-spin conformal field theories. They are not unitary, but have a variety of interesting properties. Bosonic conformal tensors have a positive-definite action, equal to the square of a field strength, and a higher-derivative gauge invariance. There exists a conserved spin-2 current (not the canonical stress tensor) defining positive central charges c and a. I calculate the values of c and a and study the operator-product structure. Higher-spin conformal spinors have no gauge invariance, admit a standard definition of c and a and can be coupled to Abelian and non-Abelian gauge fields in a renormalizable way. At the quantum level, they contribute to the one-loop beta function with the same sign as ordinary matter, admit a conformal window and non-trivial interacting fixed points. There are composite operators of high spin and low dimension, which violate the Ferrara-Gatto-Grillo theorem. Finally, other theories, such as conformal antisymmetric tensors, exhibit more severe internal problems. This research is motivated by the idea that fundamental quantum field theories should be renormalization-group (RG) interpolations between ultraviolet and infrared conformal fixed points, and quantum irreversibility should be a general principle of nature.