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Medientyp:
E-Artikel
Titel:
A symmetry algebra in double-scaled SYK
Beteiligte:
Lin, Henry W.;
Stanford, Douglas
Erschienen:
Stichting SciPost, 2023
Erschienen in:
SciPost Physics, 15 (2023) 6
Sprache:
Ohne Angabe
DOI:
10.21468/scipostphys.15.6.234
ISSN:
2542-4653
Entstehung:
Anmerkungen:
Beschreibung:
The double-scaled limit of the Sachdev-Ye-Kitaev (SYK) model takes the number of fermions and their interaction number to infinity in a coordinated way. In this limit, two entangled copies of the SYK model have a bulk description of sorts known as the “chord Hilbert space”. We analyze a symmetry algebra acting on this Hilbert space, generated by the two Hamiltonians together with a two-sided operator known as the chord number. This algebra is a deformation of the JT gravitational algebra, and it contains a subalgebra that is a deformation of the \mathfrak{sl}_2𝔰𝔩2 near-horizon symmetries. The subalgebra has finite-dimensional unitary representations corresponding to matter moving around in a discrete Einstein-Rosen bridge. In a semiclassical limit the discreteness disappears and the subalgebra simplifies to \mathfrak{sl}_2𝔰𝔩2, but with a non-standard action on the boundary time coordinate. One can make the action of \mathfrak{sl}_2𝔰𝔩2 algebra more standard at the cost of extending the boundary circle to include some “fake” portions. Such fake portions also accommodate certain subtle states that survive the semi-classical limit, despite oscillating on the scale of discreteness. We discuss applications of this algebra, including sub-maximal chaos, the traversable wormhole protocol, and a two-sided OPE.