Consistent irrelevant deformations of interacting conformal field theories

TL;DR

This paper demonstrates how to define consistent irrelevant deformations of interacting conformal field theories, which are finite or quasi-finite, and explores their conditions, examples, and potential implications for fundamental physics.

Contribution

It introduces a method to construct and analyze finite or quasi-finite irrelevant deformations of conformal field theories, including explicit examples and applications.

Findings

Deformations can be made finite or quasi-finite with coherent renormalization.

Constructed the Pauli deformation of non-Abelian Yang-Mills theory.

Developed finite chiral irrelevant deformations of superconformal theories.

Abstract

I show that under certain conditions it is possible to define consistent irrelevant deformations of interacting conformal field theories. The deformations are finite or have a unique running scale ("quasi-finite"). They are made of an infinite number of lagrangian terms and a finite number of independent parameters that renormalize coherently. The coefficients of the irrelevant terms are determined imposing that the beta functions of the dimensionless combinations of couplings vanish ("quasi-finiteness equations"). The expansion in powers of the energy is meaningful for energies much smaller than an effective Planck mass. Multiple deformations can be considered also. I study the general conditions to have non-trivial solutions. As an example, I construct the Pauli deformation of the IR fixed point of massless non-Abelian Yang-Mills theory with N_c colors and N_f <~ 11N_c/2 flavors and compute the couplings of the term F^3 and the four-fermion vertices. Another interesting application is the construction of finite chiral irrelevant deformations of N=2 and N=4 superconformal field theories. The results of this paper suggest that power-counting non-renormalizable theories might play a role in the description of fundamental physics.