Topologically shadowed quantum criticality: A non-compact conformal manifold

Tianyao Fang; Weicheng Ye; Zhengcheng Gu; Fei Zhou

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arXiv · 2604.05391

Topologically shadowed quantum criticality: A non-compact conformal manifold

Tianyao Fang·Weicheng Ye·Zhengcheng Gu·Fei Zhou

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Abstract

We propose a family of topological quantum critical points (tQCPs) separating non-invertible chiral topological orders in $(2+1)$ dimensions. We conjecture that these tQCPs can be captured by a family of scale-invariant field theories forming a non-compact scale-invariant manifold. A central feature of our proposal is topological shadowing: the underlying critical theory is rigorously constrained by the global topological data of the two adjacent gapped phases. These theories can be further projected into quantum field theories with universal non-local structures. The non-local coupling, however, controls dynamical observables along the scale-invariant manifold, including the VEV of Wilson loops and their exchange phase around the two non-contractible cycles of a torus. Despite the non-locality, our renormalization group calculations (up to two-loop order) strongly suggest that the theory shall maintain exact scale invariance. This supports, without supersymmetry, a continuous family of scale-invariant fixed points, which are further substantiated from a holographic perspective.

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Tianyao Fang, Weicheng Ye, Zhengcheng Gu, Fei Zhou. 2026-09-20. Topologically shadowed quantum criticality: A non-compact conformal manifold. https://arxiv.org/abs/2604.05391

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