Alternative to perturbative renormalization in ( 3+1 )-dimensional field theories

Perturbative renormalization provides the bedrock of understanding quantum field theories. In this work, I point out an alternative way of renormalizing quantum field theories, which is naturally encountered and well-known for the case of large <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>N</a:mi></a:math> scalar field theories. In terms of bare parameters, this nonperturbative alternative renormalization differs qualitatively from its perturbative cousin: in the continuum limit, the bare coupling constant goes to zero instead of infinity, and there is no wave-function counterterm. Despite these differences, the resulting <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>n</c:mi></c:math>-point functions of the theory are finite. I provide explicit results for alternative renormalization for the O(N) model and QCD with <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>N</e:mi><e:mi>f</e:mi></e:msub><e:mo>=</e:mo><e:mn>12</e:mn></e:math> flavors in <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mn>3</g:mn><g:mo>+</g:mo><g:mn>1</g:mn></g:mrow></g:math> dimensions. Published by the American Physical Society 2024