O realizaci Jackiw-Teitelboim gravitace

• Thesis title in Czech: O realizaci Jackiw-Teitelboim gravitace
• Thesis title in English: On the realization of Jackiw-Teitelboim gravity
• Key words: Low dimensional gravity|Black holes|Dualities|Conformal symmetry|Analog gravity
• Academic year of topic announcement: 2024/2025
• Thesis type: diploma thesis
• Department: Institute of Particle and Nuclear Physics (32-UCJF)
• Supervisor: prof. Alfredo Iorio, Ph.D.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 14.05.2024
• Date of assignment: 14.05.2024
• Confirmed by Study dept. on: 16.05.2024

Guidelines

The candidate will have knowledge of general relativity, quantum mechanics and quantum field theory. They will also know the basic of conformal symmetry, and of Lobachevsky geometry.They will then build-up knowledge on the peculiarities of low-dimensional gravity, paying attention to what remains in common with their four dimensional counterpart, especially within the two dimensional dilaton models. The focus then will be on the Jackiw-Teitelboim model, in general, and with reference to its (near) conformal symmetry. The quotient space construction, that involves very specific identifications patterns, will be their main focus. How the latter may be implemented on real laboratory circuits can be outlined.

References

C. Teitelboim, Gravitation and Hamiltonian Structure in Two Space-Time Dimensions, Phys. Lett. B 126 (1983) 415.

R. Jackiw, Lower Dimensional Gravity, Nucl. Phys. B 252 (1985) 343.

J.D. Brown, M. Henneaux and C. Teitelboim, Black holes in two spacetime dimensions, Physical Review D 33 (1986) 319.

Medhi Ameri, Jackiw-Teitelboim gravity, MSc dissertation (2021) and references therein.

T. G. Mertens, G. J. Turiaci, Solvable models of quantum black holes: a review on Jackiw-Teitelboim gravity, Living Reviews in Relativity 26 (2023) 4.

Gábor Sárosi, AdS2 holography and the SYK model, PoS(Modave2017)001.

Makoto Natsuume, AdS/CFT duality user guide, arXiv:1409.3575.

Alicia J. Kollár, Mattias Fitzpatrick & Andrew A. Houck, Hyperbolic lattices in circuit quantum electrodynamics, Nature 571 (2019) 45 arXiv:1910.12318v2 [quant-ph].

I. Boettcher, P. Bienias, R. Belyansky, A. J. Kollár, and A. V. Gorshkov, Quantum simulation of hyperbolic space with circuit quantum electrodynamics: From graphs to geometry, Phys. Rev. A 102 (2020) 032208.

G. Acquaviva, A. Iorio, P. Pais and L. Smaldone, Hunting quantum gravity with analogs: the case of graphene, Universe 8 (2022) 455.

Preliminary scope of work

The grand scenario of this work is the theoretical study of the possibility of the concrete laboratory realization of models of quantum gravity. In particular, the focus is on the duality between the 2d gravity model, known as Jackiw-Teitelboim (JT) and the 1d quantum mechanical model, known as Sachdev-Ye-Kitaev (SYK).

This duality, that is under intense investigation these days. It is presented as an example of the general correspondence between Anti de Sitter (AdS) gravity and the Conformal Field Theory (CFT) on its boundaries, known as AdS/CFT. The interest on this specific 2d/1d correspondence stems from the fact that the 1d SYK model is exactly solvable, hence many open questions on the 2d gravity side can be studied in that language.

This work will focus on the JT side of the correspondence. In particular, the candidate will elucidate the steps that take us from AdS_2, to the actual JT model. Such steps are those that, in the literature, go under the name of ‘identifications’, and are related to the quotient space construction of the 3d Banados, Teitelboim, Zanelli (BTZ) black hole. The candidate will also elucidate this aspect. In doing that, the candidate will cover the necessary material of the general theory of 2d dilaton gravity, and of this particular model, that will make them mastering the topic. Important will be the role of conformal symmetry and its breaking, and the relation of the latter with the ‘near’ realization of the AdS/CFT correspondence for JT/SYK.

The work is going to be completely theoretical. Nonetheless, its results will be of great interest for possible laboratory realizations of the JT model. Indeed, recent work has proposed that quantum fields on 2d spaces of constant negative curvature, that are the Euclidean version of AdS_2, could be realized using resonators arranged in hyperbolic lattices. By knowing the details of how AdS_2 and JT are realted, will then be of practical use in this respect.