Functional renormalization of N scalars with O(N) invariance

TL;DR

This paper explores the renormalization group flow of N scalar fields with O(N) symmetry, including nonlinear realizations, and analyzes scaling solutions with zero potential.

Contribution

It introduces flow equations for theories with linear and nonlinear O(N) symmetry and examines their scaling solutions within the derivative expansion framework.

Findings

Flow equations derived for both linear and nonlinear O(N) symmetric theories.

Identification of properties of scaling solutions with vanishing potential.

Analysis of topologically distinct realizations such as cylinders and spheres.

Abstract

We discuss general theories of N scalar fields with O(N) symmetry. In addition to the standard case of linearly realized symmetry there are also examples that carry nonlinear realizations, with the topology of a cylinder $R\times S^{N-1}$ or a sphere $S^N$. We write flow equations for the theory in the second order of the derivative expansion in the background field and discuss the properties of scaling solutions with vanishing potential.