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Peer-reviewedCC BY 4.0Journal of High Energy Physics

Thermal two-point functions in SYK and complex-time singularities

  • Ilija Burić1
  • Chi-Ming Chang2,3
  • Ivan Gusev1
  • Elizabeth Helfenberger1
  • Andrei Parnachev1
  • Mukund Rangamani4
4 affiliations
  1. 1School of Mathematics and Hamilton Mathematics Institute, Trinity College
  2. 2Tsinghua University
  3. 3Beijing Institute of Mathematical Sciences and Applications (BIMSA)
  4. 4University of California
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Abstract

A bstract : We analyze the finite-temperature two-point function of the large- N SYK model at intermediate couplings away from the infrared fixed point. Specifically, we examine its analytic structure in the complex time plane, tracking the complex-time singularities over a range of temperatures. The location of the leading singularity lies on the imaginary axis. It controls the short-time dynamics of operator complexity, defining an ‘effective temperature’ for the correlator. The next-to-leading singularity lies outside the thermal strip set by the above effective temperature. It has been argued that this could be interpreted in terms of bouncing null geodesics in the emergent black hole geometry. Both these singularities persist all the way down to zero temperature. We discuss our observations and motivate the related emergent geometry using a kinematic space perspective.

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Cite

BibTeXRIS
BibTeX
@article{buric2026thermal,
  title = {{Thermal two-point functions in SYK and complex-time singularities}},
  author = {Ilija Burić and Chi-Ming Chang and Ivan Gusev and Elizabeth Helfenberger and Andrei Parnachev and Mukund Rangamani},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = oct,
  doi = {10.1007/jhep10(2026)228},
  url = {https://link.springer.com/article/10.1007/JHEP10(2026)228},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Thermal two-point functions in SYK and complex-time singularities
AU  - Ilija Burić
AU  - Chi-Ming Chang
AU  - Ivan Gusev
AU  - Elizabeth Helfenberger
AU  - Andrei Parnachev
AU  - Mukund Rangamani
PY  - 2026
DA  - 2026/10/22
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep10(2026)228
UR  - https://link.springer.com/article/10.1007/JHEP10(2026)228
AB  - A bstract : We analyze the finite-temperature two-point function of the large- N SYK model at intermediate couplings away from the infrared fixed point. Specifically, we examine its analytic structure in the complex time plane, tracking the complex-time singularities over a range of temperatures. The location of the leading singularity lies on the imaginary axis. It controls the short-time dynamics of operator complexity, defining an ‘effective temperature’ for the correlator. The next-to-leading singularity lies outside the thermal strip set by the above effective temperature. It has been argued that this could be interpreted in terms of bouncing null geodesics in the emergent black hole geometry. Both these singularities persist all the way down to zero temperature. We discuss our observations and motivate the related emergent geometry using a kinematic space perspective.
SN  - 1029-8479
ER  -