arXiv subjects

Tianyao Fang

Publications and source records attributed to Tianyao Fang.

3 recordsLinked to original sources

arXiv2026

Topologically shadowed quantum criticality: A non-compact conformal manifold

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.

cond-mat.str-el↗

arXiv2025

The emergence of Einstein gravity from topological supergravity in $3+1$D

The topological aspects of Einstein gravity suggest that topological invariance could be a more profound principle in understanding quantum gravity. In this work, we explore a topological supergravity action that initially describes a universe without Riemann curvature, which seems trivial. However, we made a surprising discovery by introducing a small deformation parameter $λ$, which can be regarded as an AdS generalization of supersymmetry (SUSY). We find that the deformed topological quantum field theory (TQFT) becomes unstable at low energy, resulting in the emergence of a classical metric, whose dynamics are controlled by the Einstein equation. Our findings suggest that a quantum theory of gravity could be governed by a UV fixed point of a SUSY TQFT, and classical spacetime ceases to exist beyond the Planck scale.

gr-qc↗

arXiv2021

Topological gravity in 3+1D and a possible origin of dark matte

Dark matter is one of the deepest mystery of the universe. So far there is no natural explanation why the dark matter should exist and even dominate the universe. In this paper, we begin with a 3+1D topological gravity theory which is super renormalizable with vanishing beta functions, then we argue that Einstein gravity can emerge by condensing loop-like excitation from the underlying topological gravity theory. In the meanwhile, the uncondensed loop-like excitations serves as a natural candidate of dark matter and a generalized Einstein equation can be derived in the presence of loop-source(dark matter) background. Surprisingly, we find that such kind of dark matter will not contribute to scalar curvature, however, it will become a source of torsion. Finally, we derive the generalized Einstein equation in the presence of Dirac field. Very different from the usual Einstein-Carton theory, our theory further predicts that any type of normal matter, including Dirac field will not produce torsion. All these unique predictions can be tested by future experiments. Our framework suggests that topological invariant principle might play a more profound role than the well-known general covariance principle, especially towards understanding the nature of dark matter and quantum gravity in 3+1D.

gr-qc↗