Abstract
In this paper, we introduce a “partially disorder-averaged” SYK model. This model has a real parameter that smoothly interpolates between the ordinary totally disorder-averaged SYK model and the totally fixed-coupling model. For the large N effective description, in addition to the usual bi-local collective fields, we also introduce a new additional set of local collective fields. These local fields can be understood as “half” of the bi-local collective fields, and in the totally fixed-coupling limit, they represent the “half-wormholes” which were found in recent studies. We find that the large N saddles of these local fields vanish in the total-disorder-averaged limit, while they develop nontrivial profiles as we gradually fix the coupling constants. We argue that the bulk picture of these local collective fields represents a correlation between a spacetime brane and the asymptotic AdS boundary. This illuminates how the half-wormhole saddles emerge in the SYK model with fixed couplings.
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Goto, K., Suzuki, K. & Ugajin, T. Factorizing wormholes in a partially disorder-averaged SYK model. J. High Energ. Phys. 2022, 69 (2022). https://doi.org/10.1007/JHEP09(2022)069
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DOI: https://doi.org/10.1007/JHEP09(2022)069