Conformal invariance from scale invariance in non-linear sigma models

Abstract

There exists a certain argument that in even dimensions, scale invariant quantum field theories are conformal invariant. We may try to extend the argument in $2n+\epsilon$ dimensions, but the naive extension has a small loophole, which indeed shows an obstruction in non-linear sigma models in $2+\epsilon$ dimensions. Even though it could have failed due to the loophole, we show that scale invariance does imply conformal invariance of non-linear sigma models in $2+\epsilon$ dimension from the seminal work by Perelman on the Ricci flow.

arXiv comment14 pages

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Cited by in corpus (5)

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• Bootstrapping frustrated magnets: the fate of the chiral $\mathrm{O}(N)\times \mathrm{O}(2)$ universality class
• Correlators in phase-ordering from Schrödinger-invariance
• Monotonicity of RG flow in emergent dual holography of worldsheet nonlinear $\sigma$ model
• Scale without Conformal Invariance in bottom-up Holography