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This is a Quantitative Study study.

October 20, 2025Open Access

Emergent Gravity from Topological Quantum Field Theory: Stochastic Gradient Flow Perspective away from the Quantum Gravity Problem

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This new approach shows how general relativity emerges from a stochastic gradient flow, highlighting key transitions in symmetry and quantization.

The theory demonstrates that general relativity arises from a fixed point of stochastic gradient flow, showing classical characteristics.
Stochastic fluctuations vanish at the infrared limit, restoring diffeomorphism symmetries and leading to the classical Einstein-Hilbert action.
Two significant phase transitions occur, marking the breakdown of topological BF symmetries and parental symmetries of the Wilczek theory.
Quantization of the Einstein-Hilbert action becomes unnecessary, as it flows to a topological BF action with applicable non-perturbative methods.

Addazi et al. (2025) studied this question.

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This new approach shows how general relativity emerges from a stochastic gradient flow, highlighting key transitions in symmetry and quantization.