Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 9, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP09(2018)041
Keywords
Matrix Models; Integrable Field Theories; Stochastic Processes; Black Holes
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Funding
- Korea Institute for Advanced Study (KIAS) within the program IPMU-KIAS-Kyunghee Univ. joint workshop
- International Centre for Theoretical Sciences (ICTS) for participating in the program - Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology 2018 [ICTS/Prog-KAWS2018/01]
- Mandelstam Institute for Theoretical Physics within the program The Second Mandelstam Theoretical Physics School and Workshop
- International Centre for Theoretical Sciences (ICTS), Tata Institute of Fundamental Research, Bangalore
- National Research Foundation of Korea [PG058902] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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We study the onset of RMT dynamics in the mass-deformed SYK model (i.e. an SYK model deformed by a quadratic random interaction) in terms of the strength of the quadratic deformation. We use as chaos probes both the connected unfolded Spectral Form Factor (SFF) as well as the Gaussian-filtered SFF, which has been recently introduced in the literature. We show that they detect the chaotic/integrable transition of the mass-deformed SYK model at different values of the mass deformation: the Gaussian-filtered SFF sees the transition for large values of the mass deformation; the connected unfolded SFF sees the transition at small values. The latter shows a closer agreement with the transition as seen by the OTOCs. We argue that the chaotic/integrable deformation affects the energy levels inhomogeneously: for small values of the mass deformation only the low-lying states are modified while for large values of the mass deformation also the states in the bulk of the spectrum move to the integrable behavior.
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