Odd Correlations and their Gravitational Duals in the SYK Model

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Abstract/Contents

Abstract: We investigate two-point correlation functions on the Sachdev-Ye-Kitaev (SYK) model. SYK describes a system of N-Majorana fermions with random all-to-all q-couplings. In the low energy limit SYK becomes a nearly conformal theory (NCFT), which in turn has an approximate holographic dual in a nearly AdS2 or NAdS2 spacetime described by Jackiw-Teitelboim (JT) gravity. Drawing on black hole information theory guides the addition of various topological effects in the genus expansion for thermal expectation values. We compare these expected results with numerical simulations of two-point correlations for varying values of N mod 8. We see that previous correlation calculations almost perfectly account for all numeric phenomena save for an anomalous bump in the N = 4 mod 8 case and an unexpectedly high correlation plateau for N = 3 mod 8. These calculations imply the need to include higher order topologies when calculating boundary observables.

Author	Abdalla, Ahmed	https://orcid.org/0000-0003-2906-6241 (unverified)
Thesis advisor	Stanford, Douglas
Thesis advisor	Susskind, Leonard
Degree granting institution	Stanford University
Department	Department of Physics

DOI	https://doi.org/10.25740/kj095nm6578
Location	https://purl.stanford.edu/kj095nm6578

License: This work is licensed under a Creative Commons Attribution Non Commercial 4.0 International license (CC BY-NC).

Preferred citation: Abdalla, A. (2022). Odd Correlations and their Gravitational Duals in the SYK Model. Stanford Digital Repository. Available at https://purl.stanford.edu/kj095nm6578

Undergraduate Theses, Department of Physics

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