A symmetry algebra in double-scaled SYK

Journal Article · 07 December 2023 · SciPost Physics

DOI: https://doi.org/10.21468/SciPostPhys.15.6.234 · OSTI ID:2229169

Lin, Henry W.; Stanford, Douglas

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}_2 ${𝔰𝔩}_2$ 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}_2 ${𝔰𝔩}_2$ , but with a non-standard action on the boundary time coordinate. One can make the action of \mathfrak{sl}_2 ${𝔰𝔩}_2$ 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.

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0021085
• OSTI ID: 2229169
• Alternate ID(s): OSTI ID: 2319225
• Journal Information: SciPost Physics, Journal Name: SciPost Physics Journal Issue: 6 Vol. 15; ISSN 2542-4653
• Publisher: Stichting SciPostCopyright Statement
• Country of Publication: Netherlands
• Language: English