Analyticity and the Unruh effect: a study of local modular flow

Analyticity and the Unruh effect: a study of local modular flow

10 Sep 2024 | Jonathan Sorce
This paper investigates the conditions under which geometric modular flow can arise in quantum field theory. The Unruh effect is formulated as the statement that the Minkowski vacuum in a Rindler wedge has a boost as its modular flow. The paper shows that any geometric modular flow must be a conformal symmetry of the background spacetime. In a class of "weakly analytic" states, geometric modular flow must be future-directed. The paper also argues that if a geometric transformation is conformal but not isometric, it can only be realized as modular flow in a conformal field theory. The paper discusses several settings where converse results can be shown, i.e., where a state can be constructed whose modular flow reproduces a given vector field. The paper also explores the implications of analyticity for modular flow and the constraints on geometric modular flow in non-conformal theories. The paper concludes that geometric modular flow is a powerful tool for understanding the thermodynamics of quantum field theory and quantum gravity.This paper investigates the conditions under which geometric modular flow can arise in quantum field theory. The Unruh effect is formulated as the statement that the Minkowski vacuum in a Rindler wedge has a boost as its modular flow. The paper shows that any geometric modular flow must be a conformal symmetry of the background spacetime. In a class of "weakly analytic" states, geometric modular flow must be future-directed. The paper also argues that if a geometric transformation is conformal but not isometric, it can only be realized as modular flow in a conformal field theory. The paper discusses several settings where converse results can be shown, i.e., where a state can be constructed whose modular flow reproduces a given vector field. The paper also explores the implications of analyticity for modular flow and the constraints on geometric modular flow in non-conformal theories. The paper concludes that geometric modular flow is a powerful tool for understanding the thermodynamics of quantum field theory and quantum gravity.
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