Half-wormholes in SYK with one time point
In this note we study the SYK model with one time point, recently considered by Saad, Shenker, Stanford, and Yao. Working in a collective field description, they derived a remarkable identity: the square of the partition function with fixed couplings is well approximated by a "wormhole"...
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| Format: | Article |
| Language: | English |
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SciPost
2022-01-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.12.1.029 |
| _version_ | 1798022282686234624 |
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| author | Baur Mukhametzhanov |
| author_facet | Baur Mukhametzhanov |
| author_sort | Baur Mukhametzhanov |
| collection | DOAJ |
| description | In this note we study the SYK model with one time point, recently considered
by Saad, Shenker, Stanford, and Yao. Working in a collective field description,
they derived a remarkable identity: the square of the partition function with
fixed couplings is well approximated by a "wormhole" saddle plus a "pair of
linked half-wormholes" saddle. It explains factorization of decoupled systems.
Here, we derive an explicit formula for the half-wormhole contribution. It is
expressed through a hyperpfaffian of the tensor of SYK couplings. We then
develop a perturbative expansion around the half-wormhole saddle. This
expansion truncates at a finite order and gives the exact answer. The last term
in the perturbative expansion turns out to coincide with the wormhole
contribution. In this sense the wormhole saddle in this model does not need to
be added separately, but instead can be viewed as a large fluctuation around
the linked half-wormholes. |
| first_indexed | 2024-04-11T17:28:26Z |
| format | Article |
| id | doaj.art-f8cc75bfb4a946eab008418c1daa405b |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-04-11T17:28:26Z |
| publishDate | 2022-01-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-f8cc75bfb4a946eab008418c1daa405b2022-12-22T04:12:15ZengSciPostSciPost Physics2542-46532022-01-0112102910.21468/SciPostPhys.12.1.029Half-wormholes in SYK with one time pointBaur MukhametzhanovIn this note we study the SYK model with one time point, recently considered by Saad, Shenker, Stanford, and Yao. Working in a collective field description, they derived a remarkable identity: the square of the partition function with fixed couplings is well approximated by a "wormhole" saddle plus a "pair of linked half-wormholes" saddle. It explains factorization of decoupled systems. Here, we derive an explicit formula for the half-wormhole contribution. It is expressed through a hyperpfaffian of the tensor of SYK couplings. We then develop a perturbative expansion around the half-wormhole saddle. This expansion truncates at a finite order and gives the exact answer. The last term in the perturbative expansion turns out to coincide with the wormhole contribution. In this sense the wormhole saddle in this model does not need to be added separately, but instead can be viewed as a large fluctuation around the linked half-wormholes.https://scipost.org/SciPostPhys.12.1.029 |
| spellingShingle | Baur Mukhametzhanov Half-wormholes in SYK with one time point SciPost Physics |
| title | Half-wormholes in SYK with one time point |
| title_full | Half-wormholes in SYK with one time point |
| title_fullStr | Half-wormholes in SYK with one time point |
| title_full_unstemmed | Half-wormholes in SYK with one time point |
| title_short | Half-wormholes in SYK with one time point |
| title_sort | half wormholes in syk with one time point |
| url | https://scipost.org/SciPostPhys.12.1.029 |
| work_keys_str_mv | AT baurmukhametzhanov halfwormholesinsykwithonetimepoint |