For a free scalar in 2+1 dimensions with a quadratic null cut, modular flow is local only in symmetric limits; the full nonlocal flow satisfies an integral-differential equation and breaks the local-boost picture at λ = α x^- e^(2πs) ~ 1.
Maldacena, The large-N limit of superconformal field theories and supergravity , International Journal of Theoretical Physics 38 (1999) 1113
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Non-local modular flows across deformed null-cuts
For a free scalar in 2+1 dimensions with a quadratic null cut, modular flow is local only in symmetric limits; the full nonlocal flow satisfies an integral-differential equation and breaks the local-boost picture at λ = α x^- e^(2πs) ~ 1.