# Symmetry breaking and RG flows with higher dimensional operators

## TL;DR

This paper explores how higher dimensional operators influence symmetry breaking and renormalization group flows in scalar field theories, highlighting the importance of basis choice and reparametrization effects.

## Contribution

It demonstrates the mapping of RG flows between different operator bases and discusses the impact of ghosts on stability and symmetry breaking.

## Key findings

- RG flows depend on operator basis choice
- Reparametrization ghosts affect stability analysis
- Higher dimensional operators influence phase diagrams

## Abstract

We discuss the role of higher dimensional operators in the spontaneous breaking of internal symmetry and scale invariance, in the context of the Lorentz invariant scalar field theory. Using the $\varepsilon$-expansion we determine phase diagrams and demonstrate that (un)stable RG flows computed with a certain basis of dimension 6 operators in the Lagrangian, map to (un)stable RG flows of another basis related to the first by field redefinitions. Crucial is the presence of reparametrization ghosts if Ostrogradsky ghosts appear.