Parisi-Sourlas Supertranslation and Scale without Conformal symmetry

Yu Nakayama

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arXiv · 2411.12934

Parisi-Sourlas Supertranslation and Scale without Conformal symmetry

Yu Nakayama

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Abstract

Inspired by the possibility of emergent supersymmetry in critical random systems, we study a field theory model with a quartic potential of one superfield, possessing the Parisi-Sourlas supertranslation symmetry. Within perturbative $\epsilon$ expansion, we find nine non-trivial scale invariant renormalization group fixed points, but only one of them is conformal. We, however, believe scale invariance without conformal invariance cannot occur without a sophisticated mechanism because it predicts the existence of a non-conserved but non-renormalized vector operator called virial current, whose existence must be non-generic. We show that the virial current in this model is related to the supercurrent by supertranslation. The supertranslation Ward-Takahashi identity circumvents the genericity argument, explaining its non-renormalization property.

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Yu Nakayama. 2024-11-19. Parisi-Sourlas Supertranslation and Scale without Conformal symmetry. https://arxiv.org/abs/2411.12934

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