TY - JOUR
T1 - A proposal for 3d quantum gravity and its bulk factorization
AU - Mertens, Thomas G.
AU - Simón, Joan
AU - Wong, Gabriel
N1 - Funding Information:
We would like to thank Nezhla Aghaei, Alexandre Belin, Andreas Blommaert, Andreas Brauer, Daniel Jafferis, Daniel Kapec, David Kolchmeyer, Alex Maloney, Samir Mathur, Du Pei, Ingo Runkel, and Shinsei Ryu for discussions related to this work. GW especially thanks David Kolchmeyer and Daniel Jafferis for extended discussions on related topics. TM was supported by Research Foundation Flanders (FWO Vlaanderen), and acknowledges financial support from the European Research Council (grant BHHQG-101040024). Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. JS is supported by the Science and Technology Facilities Council [grant number ST/T000600/1]. GW would like to thank the Aspen center for physics for hospitality while this work was being completed.
Funding Information:
We would like to thank Nezhla Aghaei, Alexandre Belin, Andreas Blommaert, Andreas Brauer, Daniel Jafferis, Daniel Kapec, David Kolchmeyer, Alex Maloney, Samir Mathur, Du Pei, Ingo Runkel, and Shinsei Ryu for discussions related to this work. GW especially thanks David Kolchmeyer and Daniel Jafferis for extended discussions on related topics. TM was supported by Research Foundation Flanders (FWO Vlaanderen), and acknowledges financial support from the European Research Council (grant BHHQG-101040024). Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. JS is supported by the Science and Technology Facilities Council [grant number ST/T000600/1]. GW would like to thank the Aspen center for physics for hospitality while this work was being completed.
Publisher Copyright:
© 2023, The Author(s).
PY - 2023/6/22
Y1 - 2023/6/22
N2 - Recent progress in AdS/CFT has provided a good understanding of how the bulk space-time is encoded in the entanglement structure of the boundary CFT. However, little is known about how spacetime emerges directly from the bulk quantum theory. We address this question in an effective 3d quantum theory of pure gravity, which describes the high temperature regime of a holographic CFT. This theory can be viewed as a q-deformation and dimensional uplift of JT gravity. Using this model, we show that the Bekenstein-Hawking entropy of a two-sided black hole equals the bulk en-tanglement entropy of gravitational edge modes. In the conventional Chern-Simons description, these black holes correspond to Wilson lines in representations of PSL(2, R) ⊗ PSL(2, R). We show that thecorrect calculation of gravitational entropy suggests we should interpret the bulk theory as an extended topological quantum field theory associated to the quantum semi-group SL⁺(2, R) ⊗ SL⁺(2, R). Our calculation suggests an effective description of bulk microstates in terms of collective, anyonic degrees of freedom whose entanglement leads to the emergence of the bulk spacetime.
AB - Recent progress in AdS/CFT has provided a good understanding of how the bulk space-time is encoded in the entanglement structure of the boundary CFT. However, little is known about how spacetime emerges directly from the bulk quantum theory. We address this question in an effective 3d quantum theory of pure gravity, which describes the high temperature regime of a holographic CFT. This theory can be viewed as a q-deformation and dimensional uplift of JT gravity. Using this model, we show that the Bekenstein-Hawking entropy of a two-sided black hole equals the bulk en-tanglement entropy of gravitational edge modes. In the conventional Chern-Simons description, these black holes correspond to Wilson lines in representations of PSL(2, R) ⊗ PSL(2, R). We show that thecorrect calculation of gravitational entropy suggests we should interpret the bulk theory as an extended topological quantum field theory associated to the quantum semi-group SL⁺(2, R) ⊗ SL⁺(2, R). Our calculation suggests an effective description of bulk microstates in terms of collective, anyonic degrees of freedom whose entanglement leads to the emergence of the bulk spacetime.
U2 - 10.1007/JHEP06(2023)134
DO - 10.1007/JHEP06(2023)134
M3 - Article
SN - 1126-6708
VL - 2023
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
M1 - 134
ER -