A convergent genus expansion for the plateau

• URL: http://arxiv.org/abs/2210.11565v1
• Date: Thu, 20 Oct 2022 20:00:49 GMT
• Title: A convergent genus expansion for the plateau
• Authors: Phil Saad, Douglas Stanford, Zhenbin Yang, Shunyu Yao
• Abstract summary: We conjecture a formula for the spectral form factor of a double-scaled matrix integral in the limit of large time, large density of states, and fixed temperature. At genus one we show how the full moduli space integral resolves the low energy region and gives a finite nonzero answer.
• Score: 4.991963552834892
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We conjecture a formula for the spectral form factor of a double-scaled matrix integral in the limit of large time, large density of states, and fixed temperature. The formula has a genus expansion with a nonzero radius of convergence. To understand the origin of this series, we compare to the semiclassical theory of "encounters" in periodic orbits. In Jackiw-Teitelboim (JT) gravity, encounters correspond to portions of the moduli space integral that mutually cancel (in the orientable case) but individually grow at low energies. At genus one we show how the full moduli space integral resolves the low energy region and gives a finite nonzero answer.

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