Derivation of the two Schwarzians effective action for the Sachdev–Ye-Kitaev spectral form factor

The Sachdev–Ye-Kitaev model spectral form factor exhibits absence of information loss, in the form of a ramp and a plateau that are typical in random matrix theory. In a large N collective fields description, the ramp was reproduced by Saad et al. (A semiclassical ramp in SYK and in gravity, arXiv:1...

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Bibliographic Details
Published in:The European physical journal. C, Particles and fields Particles and fields, 2022-06, Vol.82 (6), p.1-17, Article 559
Main Author: Cardella, Matteo A.
Format: Article
Language:English
Subjects:
Astronomy
Astrophysics and Cosmology
Black holes
Broken symmetry
Elementary Particles
Entropy
Form factors
Gravity
Hadrons
Heavy Ions
Hilbert space
Matrix theory
Measurement Science and Instrumentation
Nuclear Energy
Nuclear Physics
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Regular Article - Theoretical Physics
Saddles
String Theory
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Summary:The Sachdev–Ye-Kitaev model spectral form factor exhibits absence of information loss, in the form of a ramp and a plateau that are typical in random matrix theory. In a large N collective fields description, the ramp was reproduced by Saad et al. (A semiclassical ramp in SYK and in gravity, arXiv:1806.06840 ) by replica symmetry breaking saddles. We derive a two sides Schwarzians effective action for fluctuations around the ramp critical saddles, by computing responses to a smeared version of the two replica kinetic kernel. Our result confirms [1], where the form of the action was heuristically guessed by indirect arguments supported by numerical evidences.
ISSN:1434-6052
1434-6044
1434-6052
DOI:10.1140/epjc/s10052-022-10491-x