Virasoro algebras, kinematic space and the spectrum of modular Hamiltonians in CFT2

Abstract

We construct an infinite class of eigenmodes with integer eigenvalues for the Vacuum Modular Hamiltonian of a single interval N in 2d CFT and study some of its interesting properties, which includes its action on OPE blocks as well as its bulk duals. Our analysis suggests that these eigenmodes, like the OPE blocks have a natural description on the so called kinematic space of CFT2 and in particular realize the Virasoro algebra of the theory on this kinematic space. Taken together, our results hints at the possibility of an effective description of the CFT2 in the kinematic space language.

Virasoro Entanglement Berry Phases

“…We refer to Appendix C for a discussion of these issues in the case of the Virasoro algebra. For this reason, we will consider a different class of transformations, i.e., those which diagonalize the adjoint action of the modular Hamiltonian H mod (see [30] where a similar diagonalization in terms of so-called modular eigenmodes was considered). Therefore, we start from the eigenvalue equation…”