A symmetry algebra in double-scaled SYK

A symmetry algebra in double-scaled SYK

Blog Article

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 alphaville clothing chord number.

This algebra is a deformation of the JT gravitational algebra, and it contains a subalgebra that is a deformation of the $mathfrak{sl}_2$ 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 $mathfrak{sl}_2$, but with a non-standard action on the boundary time coordinate.

One can make the action of $mathfrak{sl}_2$ 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 iphone 14 price san francisco discuss applications of this algebra, including sub-maximal chaos, the traversable wormhole protocol, and a two-sided OPE.