beta-functions in higher dimensional field theories

TL;DR

This paper reviews recent progress in calculating renormalization group functions for scalar and gauge theories in six and higher dimensions, confirming their universality and consistency with large N expansion results.

Contribution

It provides a comprehensive review of the construction of RG functions in higher-dimensional theories, highlighting their agreement with known critical exponents.

Findings

RG functions constructed for higher-dimensional theories

Critical exponents match large N expansion results

Theories lie in their universality classes at the Wilson-Fisher fixed point

Abstract

We review recent activity in the construction of the renormalization group functions for O(N) scalar and gauge theories in six and higher dimensions. The theories lie in their respective universality classes at the Wilson-Fisher fixed point. The critical exponents at this fixed point in the various dimensions are all in agreement with the known exponents determined in the large Nexpansion.