TY - JOUR

T1 - Reducing the O(3) model as an effective field theory

AU - Gudnason, Sven Bjarke

AU - Nitta, Muneto

N1 - Publisher Copyright:
© 2022, The Author(s).

PY - 2022/3

Y1 - 2022/3

N2 - We consider the O(3) or ℂP1 nonlinear sigma model as an effective field theory in a derivative expansion, with the most general Lagrangian that obeys O(3), parity and Lorentz symmetry. We work out the complete list of possible operators (terms) in the Lagrangian and eliminate as many as possible using integrations by parts. We further show at the four-derivative level, that the theory can be shown to avoid the Ostrogradsky instability, because the dependence on the d’Alembertian operator or so-called box, can be eliminated by a field redefinition. Going to the six-derivative order in the derivative expansion, we show that this can no longer be done, unless we are willing to sacrifice Lorentz invariance. By doing so, we can eliminate all dependence on double time derivatives and hence the Ostrogradsky instability or ghost, however, we unveil a remaining dynamical instability that takes the form either as a spiral instability or a runaway instability and estimate the critical field norm, at which the instability sets off.

AB - We consider the O(3) or ℂP1 nonlinear sigma model as an effective field theory in a derivative expansion, with the most general Lagrangian that obeys O(3), parity and Lorentz symmetry. We work out the complete list of possible operators (terms) in the Lagrangian and eliminate as many as possible using integrations by parts. We further show at the four-derivative level, that the theory can be shown to avoid the Ostrogradsky instability, because the dependence on the d’Alembertian operator or so-called box, can be eliminated by a field redefinition. Going to the six-derivative order in the derivative expansion, we show that this can no longer be done, unless we are willing to sacrifice Lorentz invariance. By doing so, we can eliminate all dependence on double time derivatives and hence the Ostrogradsky instability or ghost, however, we unveil a remaining dynamical instability that takes the form either as a spiral instability or a runaway instability and estimate the critical field norm, at which the instability sets off.

KW - Effective Field Theories

KW - Sigma Models

UR - http://www.scopus.com/inward/record.url?scp=85126192111&partnerID=8YFLogxK

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U2 - 10.1007/JHEP03(2022)030

DO - 10.1007/JHEP03(2022)030

M3 - Article

AN - SCOPUS:85126192111

VL - 2022

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 3

M1 - 30

ER -