Abstract
A feature the \( \mathcal{N} \) = 2 supersymmetric Sachdev-Ye-Kitaev (SYK) model shares with extremal black holes is an exponentially large number of ground states that preserve supersymmetry. In fact, the dimension of the ground state subsector is a finite fraction of the total dimension of the SYK Hilbert space. This fraction has a remarkably simple bulk interpretation as the probability that the zero-temperature wormhole — a supersymmetric Einstein-Rosen bridge — has vanishing length. Using chord techniques, we compute the zero-temperature Hartle-Hawking wavefunction; the results reproduce the ground state count obtained from boundary index computations, including non-perturbative corrections. Along the way, we improve the construction [1] of the super-chord Hilbert space and show that the transfer matrix of the empty wormhole enjoys an enhanced \( \mathcal{N} \) = 4 supersymmetry. We also obtain expressions for various two point functions at zero temperature. Finally, we find the expressions for the supercharges acting on more general wormholes with matter and present the superchord algebra.
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Acknowledgments
We thank Pawel Caputa, Luca Iliesiu, Sonja Klisch, Juan Maldacena, Henry Maxfield, Stephen Shenker, Douglas Stanford, and Zhenbin Yang for helpful discussions. JB is supported by the NCN Sonata Bis 9 2019/34/E/ST2/00123 grant. JB wants to give special thanks to Douglas Stanford and the Stanford Institute for Theoretical Physics for generous hospitality and support during his visit at Stanford University, where this work was initiated. HL is supported by a Bloch Fellowship. CY wants to give special thanks to Douglas Stanford and Shunyu Yao for helping her get through difficult times in life which coincided with when this work was initiated.
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Boruch, J., Lin, H.W. & Yan, C. Exploring supersymmetric wormholes in \( \mathcal{N} \) = 2 SYK with chords. J. High Energ. Phys. 2023, 151 (2023). https://doi.org/10.1007/JHEP12(2023)151
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DOI: https://doi.org/10.1007/JHEP12(2023)151