Abstract
Implications are explored of promoting non-conformal scale-invariant theories to conformal theories by nonlinearly realizing the missing symmetry. Properties of the associated Nambu-Goldstone mode imply that conformal invariance cannot be spontaneously broken to scale invariance in unitary theories and that, as well known, scale invariant unitary theories in two dimensions are also conformal. The promoted theories have only conformal primaries and no descendants. The (non-)decoupling of the Nambu-Goldstone mode is explicitly shown in examples of scale invariant theories that are actually (not) conformal.
Highlights
I explore the implications of promoting nonconformal scale-invariant theories to conformal theories by nonlinearly realizing the missing symmetry
A long-standing fundamental question in conformal field theory is whether conformal invariance follows from mere scale invariance
I will assume that a scale invariant field theory exists that is not conformally invariant and explore promoting it to a conformally invariant theory by introducing a Nambu-Goldstone (NG) mode and nonlinearly realizing the action of the coset fConformalg=fScaleg, ala the Callan-ColemanWess-Zumino formalism [9] suitably adapted to the breaking of a spacetime symmetry [10]. (Poincareinvariance will be assumed throughout, so this should be distinguished from the “pseudoconformal” scenario [11].)
Summary
Realized conformal invariance in scale invariant field theories Takemichi Okui*. I will assume that a scale invariant field theory exists that is not conformally invariant and explore promoting it to a conformally invariant theory by introducing a Nambu-Goldstone (NG) mode and nonlinearly realizing the action of the coset fConformalg=fScaleg, ala the Callan-ColemanWess-Zumino formalism [9] suitably adapted to the breaking of a spacetime symmetry [10]. I hope that some incarnations of the properties of the NG mode and peculiarities of the promoted theories might turn out to be key elements of an eventual proof that scale invariance implies conformal invariance Until such a proof is provided, the present formalism may be useful for phenomenological studies of nonconformal scale invariance, assuming that such a theory exists. The present coset (1) has been studied in [13,14,15] for unbroken conformal group as that is
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