Virasoro algebra from modular Hamiltonians
Year: 2021
Type: preprint
Abstract: We construct an infinite class of eigen modes with integer eigenvalues for the Vacuum Modular Hamiltonian of a single interval in 2d CFT. An interesting feature of this construction is that these eigen modes together with the Modular Hamiltonian form a Virasoro algebra. The construction is geometric in the sense that it is intimately related to the partition of the interval ($N$) into subintervals ($N'$) and ($N''$). In particular, we show that given a set consisting of a causal diamond associated to an interval ($N$) and its sub-intervals ($N'$, $N''$) on a constant time slice in a 2d CFT, one can construct modular eigen modes, satisfying the Virasoro algebra, which we call the 'modular Virasoro algebra'. For ($n=\pm 1, 0$), the corresponding generators are related to the modular Hamiltonians of the interval and its sub intervals. Another interesting feature of our construction is that OPE blocks associated with the interval $N$ transform as the modes of the primary highest weight field under transformations generated by these 'modular Virasoro generators'. We end with some comments on the bulk dual of the modular Virasoro algebra.
Source: arXiv (Cornell University)
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3121680592