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Modular flow is a symmetry of the algebra of observables associated to spacetime regions. It has played a key role in recent connections between information theory, QFT and gravity. However, little is known about its explicit action beyond highly symmetric cases. The key new element presented in this talk is a new formula for modular flows for free chiral fermions in 1+1 dimensions. This is obtained from the resolvent, a standard technique in complex analysis. We present novel results -- not fixed by conformal symmetry -- for disjoint regions on the plane, cylinder and torus. Depending on temperature and boundary conditions, these display different behaviour ranging from purely local to non-local in relation to the mixing of operators at spacelike separation. We also discuss the modular two-point function, whose analytic structure is in precise agreement with the KMS condition that governs modular evolution. The ready-to-use formulae presented may provide new ingredients to explore the connection between spacetime and entanglement.
Based on 2008.07532