In 2d CFTs, every suitably regular Unruh flow on the Rindler wedge is the modular flow of a state obtained by a conformal unitary acting on the vacuum or thermal state, and local entropy and stress-tensor formulas follow.
Bootstrap 2024: Lectures on "The algebraic approach: when, how, and why?"
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abstract
These lecture notes formed the basis of a mini-course on algebraic quantum field theory presented at the Bootstrap 2024 conference in Madrid. The goal of the notes is to explain the merits of algebraic quantum field theory to a broad audience, and to explore (i) how to know when a particular question calls for an algebraic answer, (ii) how to apply the tools of algebraic QFT to such a problem, and (iii) why quantum field theorists of all stripes stand to benefit from a basic knowledge of algebraic quantum fields. The first lecture focuses on the big-picture motivation behind the algebraic approach to quantum field theory, and an elaboration of its basic tools. Subsequent lectures explain some of the modern achievements of the algebraic toolkit, including an argument for the averaged null energy condition and an enhanced understanding of entropy for semiclassical black holes.
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Geometric modular flows in 2d CFT and beyond
In 2d CFTs, every suitably regular Unruh flow on the Rindler wedge is the modular flow of a state obtained by a conformal unitary acting on the vacuum or thermal state, and local entropy and stress-tensor formulas follow.