# Gravity, Quantum Fields and Information

How do gravity and matter at any point in space emerge from an underlying microscopic reality? How can we model complex quantum mechanical systems with many constituents? What happens at a microscopic level when such systems evolve in time, and how can we quantify it? These are some of the motivating questions for the independent research group on “Gravity, Quantum Fields and Information” (GQFI) led by Dr. Michal P. Heller and generously supported by the Humboldt Foundation through the Sofja Kovalevskaja Award.

The theoretical framework underlying these questions is the holographic principle, a set of ideas originating from the field of black hole physics which seek the origin of the gravitational force and the universe as a whole in terms of a lower-dimensional reality without gravitational interactions. In 1997 these ideas led to a very precise correspondence. On the one side, it involved some negatively curved universes, and on the other a certain class of quantum field theories in a lower number of dimensions. This holography, also known as the AdS/CFT or the gauge/gravity duality, with time became a valuable ab-initio approach to quantum field theories.

Quantum dynamics in closed systems away from equilibrium is relevant to a vast array of problems: heavy-ion collisions, cold atom quenches, the physics of the expanding universe, quantum thermodynamics, and the black hole information problem. The gauge/gravity duality allowed modeling equilibration processes similar to the ones occurring in ultra-energetic collisions of atomic nuclei at RHIC and LHC accelerators, and has brought many interesting phenomenological lessons in the field of nuclear physics [1-3]. In the context of critical quantum quenches, investigations both within the gauge-gravity duality [4] and in integrable lattice models [5] led to the discovery of new scaling regimes and provided new interpretations to known scalings. Additionally, in the context of quantum thermodynamics, scaling laws have been derived for the trace square distance [6], which sheds further light on the approach to equilibrium for excited quantum states.

A breakthrough result in 2006 demonstrated (see also [7]) that a very important role in the way negatively curved universes emerge from underlying quantum field theories is played by the information about entanglement between different sub-regions in these systems. The latter topic is the focal point of interest for quantum-many body physics and, cleverly used, allows for efficient simulations of complex quantum systems with many constituents. Furthermore, thinking about the physics of entanglement in quantum field theories has led to a fascinating link with other spacetimes, in particular the de Sitter geometry of our expanding Universe [8-9].

Other ideas from quantum information such as quantum error correction have also proven fruitful for understanding how information is encoded in holography [10]. One outstanding question is how local bulk physics -- that is, spacetime itself -- emerges from the boundary CFT. In general (non-vacuum) geometries, holographic shadows represent barriers to naive reconstruction attempts [11]. This suggests that something beyond entanglement may be necessary to fully reconstruct spacetime, particularly in the interior of black holes. A promising proposal is “holographic complexity”, which we are only just beginning to understand [12,13]. More generally, understanding the deeper relationship between gravity and quantum information will likely provide important lessons for quantum gravity, and may also be crucial in resolving various puzzles in this regard; e.g., the firewall paradox [14].

In addition to real space, quantum entanglement may also be present in non-geometric bipartitionings of the Hilbert space, universal contributions of which were computed in [15]. Through the bulk/edge correspondence, this gives an alternative interpretation to topological entanglement entropy of quantum systems ranging from black holes to topologically ordered many body systems, symmetry-enriched versions of which have also been realized (see [16]).

The aim of the GQFI independent research group is to explore the fascinating intersection of gravitational and high-energy physics with quantum information science. The topics of primary interest are equilibration phenomena in quantum field theories, the broadly-understood link between spacetime geometries and entanglement, and entanglement-based approaches to quantum field theories.

## References:

[1] M. P. Heller, R. A. Janik, P. Witaszczyk, “The characteristics of thermalization of boost-invariant plasma from holography,” Phys. Rev. Lett. 108 (2012) 201602, arXiv:1103.3452 [hep-th]

[2] M. P. Heller, D. Mateos, W. van der Schee, D. Trancanelli, “Strong Coupling Isotropization of Non-Abelian Plasmas Simplified,” Phys. Rev. Lett. 108 (2012) 191601, arXiv:1202.0981 [hep-th]

[3] M. P. Heller, R. A. Janik, P. Witaszczyk, “Hydrodynamic Gradient Expansion in Gauge Theory Plasmas,” Phys. Rev. Lett. 110 (2013) 211602, arXiv:1302.0697 [hep-th]

[4] P. Basu, D. Das, S. R. Das, T. Nishioka, "Quantum quench across a zero temperature holographic superfluid transition", JHEP 03 (2013) 146, arXiv:1211.7076 [hep-th]

[5] D. Das, S. R. Das, D. A. Galante, R. C. Myers, K. Sengupta, "An exactly solvable quench protocol for integrable spin models", arXiv:1706.02322 [hep-th]

[6] P. Basu, D. Das, S. Datta and S. Pal, "Thermality of eigenstates in conformal field theories", Phys. Rev. E 96 (2017) no. 02 022149, arXiv:1705.03001 [hep-th]

[7] V. Balasubramanian, B. D. Chowdhury, B. Czech, J. de Boer, M. P. Heller, “Bulk curves from boundary data in holography,” Phys. Rev. D89 (2014), 086004, arXiv:1310.4204 [hep-th]

[8] J. de Boer, M. P. Heller, R. C. Myers, Y. Neiman, “Holographic de Sitter Geometry from Entanglement in Conformal Field Theory,” Phys. Rev. Lett. 116 (2016), 061602, arXiv:1509.00113 [hep-th]

[9] J. de Boer, F. M. Haehl, M. P. Heller, R. C. Myers, “Entanglement, holography and causal diamonds,” JHEP 1608 (2016) 162, arXiv:1606.03307 [hep-th]

[10] B. Freivogel, R. A. Jefferson, L. Kabir, “Precursors, Gauge Invariance, and Quantum Error Correction in AdS/CFT”, JHEP 04 (2016) 119, arXiv:1602.04811 [hep-th]

[11] B. Freivogel, R. A. Jefferson, L. Kabir, B. Mosk, I-S. Yang, “Casting Shadows on Holographic Reconstruction”, Phys. Rev. D91, arXiv:1412.5175 [hep-th]

[12] R. A. Jefferson, R. C. Myers, “Circuit complexity in quantum field theory”, arXiv:1707.08570 [hep-th]

[13] S. Chapman, M. P. Heller, H. Marrochio, F. Pastawski, “Towards Complexity for Quantum Field Theory States”, arXiv:1707.08582 [hep-th]

[14] B. Freivogel, R. A. Jefferson, L. Kabir, I-S. Yang, “Geometry of the Infalling Causal Patch”, Phys. Rev. D91, arXiv:1406.6043 [hep-th]

[15] D. Das and S. Datta, "Universal features of left-right entanglement entropy", Phys. Rev. Lett. 115 (2015), no. 13 131602, arXiv:1504.02475 [hep-th]

[16] D. Ben-Zion, D. Das, J. A. McGreevy, "Exactly solvable models of spin liquids with spinons, and of three-dimensional topological paramagnets", Phys. Rev. B 93 (2016), no. 15 155147, arXiv:1511.01539 [hep-th]