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Peer-reviewedCC BYPhysics Letters B

Emergent gravity from topological quantum field theory: Stochastic gradient flow perspective away from the quantum gravity problem

  • Andrea Addazi1,2
  • Salvatore Capozzıello3,4,5,6
  • Jinglong Liu7,8,9,10
  • Antonino Marcianò7,8,11,2
  • Giuseppe Meluccio4,6
  • Xuanlin Su7,8
11 affiliations
  1. 1Institute of Astronomy and Astrophysics, School of Mathematics and Physics, Anqing Normal University, Anqing, 246133, China
  2. 2Laboratori Nazionali di Frascati INFN, Frascati, Rome, Italy
  3. 3Dipartimento di Fisica “E. Pancini”, Università di Napoli “Federico II”, Via Cinthia 9, Napoli, 80126, Italy
  4. 4INFN Sezione di Napoli, Complesso Universitario di Monte Sant’Angelo, Edificio 6, Via Cintia, Napoli, 80126, Italy
  5. 5Research Center of Astrophysics and Cosmology, Khazar University, 41 Mehseti Street, Baku, AZ1096, Azerbaijan
  6. 6Scuola Superiore Meridionale, Largo San Marcellino, 10, Napoli, 80138, Italy
  7. 7Center for Astronomy and Astrophysics, Fudan University, Shanghai, 200433, China
  8. 8Center for Field Theory and Particle Physics & Department of Physics, Fudan University, Shanghai, 200433, China
  9. 9School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, 200240, China
  10. 10Tsung-Dao Lee Institute, 1 Lisuo Road, Shanghai, 201210, China
  11. 11INFN sezione di Roma “Tor Vergata”, Rome, 00133, Italy
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Abstract

We propose a scenario according to which the ultraviolet completion of General Relativity is realized through a stochastic gradient flow towards a topological BF theory. Specifically, we consider the stochastic gradient flow of a pre-geometric theory proposed by Wilczek. Its infrared limit exists, and corresponds to a fixed point where stochastic fluctuations vanish. Diffeomorphism symmetries are restored in this limit, where the theory is classical and expressed by the Einstein-Hilbert action. The infrared phase then corresponds to the classical theory of General Relativity, the quantization of which becomes meaningless. Away from the infrared limit, in the pre-geometric phase of the stochastic gradient flow, the relevant fields of the Wilczek theory undergo stochastic fluctuations. The theory can be quantized perturbatively, generating corrections to the classical Einstein-Hilbert action. The stochastic gradient flow also possesses an ultraviolet fixed point. The theory flows to a topological BF action, to which non-perturbative quantization methods can be applied. Two phase transitions occur along the thermal time dynamics, being marked by: i) the breakdown of the topological BF symmetries in the ultraviolet regime, which originates the pre-geometric phase described by the Wilczek theory; ii) the breakdown of the parental symmetries characterizing the Wilczek theory, from which General Relativity emerges. The problem of quantizing the Einstein-Hilbert action of gravity finally becomes redundant.

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Cite

BibTeXRIS
BibTeX
@article{addazi2026emergent,
  title = {{Emergent gravity from topological quantum field theory: Stochastic gradient flow perspective away from the quantum gravity problem}},
  author = {Andrea Addazi and Salvatore Capozzıello and Jinglong Liu and Antonino Marcianò and Giuseppe Meluccio and Xuanlin Su},
  journal = {Physics Letters B},
  year = {2026},
  month = jun,
  doi = {10.1016/j.physletb.2026.140576},
  url = {https://doi.org/10.1016/j.physletb.2026.140576},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Emergent gravity from topological quantum field theory: Stochastic gradient flow perspective away from the quantum gravity problem
AU  - Andrea Addazi
AU  - Salvatore Capozzıello
AU  - Jinglong Liu
AU  - Antonino Marcianò
AU  - Giuseppe Meluccio
AU  - Xuanlin Su
PY  - 2026
DA  - 2026/06/01
JO  - Physics Letters B
DO  - 10.1016/j.physletb.2026.140576
UR  - https://doi.org/10.1016/j.physletb.2026.140576
AB  - We propose a scenario according to which the ultraviolet completion of General Relativity is realized through a stochastic gradient flow towards a topological BF theory. Specifically, we consider the stochastic gradient flow of a pre-geometric theory proposed by Wilczek. Its infrared limit exists, and corresponds to a fixed point where stochastic fluctuations vanish. Diffeomorphism symmetries are restored in this limit, where the theory is classical and expressed by the Einstein-Hilbert action. The infrared phase then corresponds to the classical theory of General Relativity, the quantization of which becomes meaningless. Away from the infrared limit, in the pre-geometric phase of the stochastic gradient flow, the relevant fields of the Wilczek theory undergo stochastic fluctuations. The theory can be quantized perturbatively, generating corrections to the classical Einstein-Hilbert action. The stochastic gradient flow also possesses an ultraviolet fixed point. The theory flows to a topological BF action, to which non-perturbative quantization methods can be applied. Two phase transitions occur along the thermal time dynamics, being marked by: i) the breakdown of the topological BF symmetries in the ultraviolet regime, which originates the pre-geometric phase described by the Wilczek theory; ii) the breakdown of the parental symmetries characterizing the Wilczek theory, from which General Relativity emerges. The problem of quantizing the Einstein-Hilbert action of gravity finally becomes redundant.
SN  - 0370-2693
SN  - 1873-2445
ER  -