Symmetry breaking and RG flows with higher dimensional operators

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 $\epsilon$-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.

arXiv commentpublished version

References in corpus (14)

• Dimension-Six Terms in the Standard Model Lagrangian
• Causality, Analyticity and an IR Obstruction to UV Completion
• Renormalization Group Evolution of the Standard Model Dimension Six Operators I: Formalism and lambda Dependence
• Reduced Effective Lagrangians
• Feynman Rules for the Standard Model Effective Field Theory in $R_{\xi }$-gauges
• Scheming in the SMEFT... and a reparameterization invariance!
• Field redefinitions in effective theories at higher orders
• Renormalization group equations for effective field theories
• Effective Beta-Functions for Effective Field Theory
• Electroweak Symmetry Breaking without the ${\mu }^2$ Term
• Multi-critical ${\square }^k$ scalar theories: A perturbative RG approach with $\epsilon$-expansion
• Euclidean scalar field theory in the bi-local approximation
• XEFT, the challenging path up the hill: dim = 6 and dim = 8
• Wilson-Fisher fixed points for any dimension

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