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Entropic g Theorem in General Spacetime Dimensions.

Horacio Casini1, Ignacio Salazar Landea2, Gonzalo Torroba1

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Renormalization group flows on defects in conformal field theories are irreversible. Impurity entropy, identified with quantum relative entropy, monotonically decreases, providing an information-theoretic basis for this irreversibility.

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Area of Science:

  • Theoretical physics
  • Quantum field theory
  • Conformal field theory

Background:

  • Renormalization group (RG) flows describe how physical systems change with scale.
  • Understanding RG flow irreversibility is crucial in quantum field theory.
  • Pointlike defects in conformal field theories offer a simplified framework to study RG dynamics.

Purpose of the Study:

  • To establish the irreversibility of renormalization group flows on pointlike defects.
  • To identify the impurity entropy with quantum relative entropy.
  • To provide an information-theoretic interpretation of RG flow irreversibility.

Main Methods:

  • Analyzing renormalization group flows on pointlike defects in d-dimensional Lorentzian conformal field theories.
  • Equating impurity entropy (g) with quantum relative entropy through two distinct methods.
  • Utilizing a null deformation of the Cauchy surface.
  • Employing a local quench protocol.

Main Results:

  • The irreversibility of renormalization group flows on pointlike defects is rigorously established.
  • Impurity entropy (g) is shown to be equivalent to quantum relative entropy via two novel approaches.
  • Positivity and monotonicity of relative entropy directly imply the monotonic decrease of g along RG flows.

Conclusions:

  • The study provides a clear information-theoretic meaning for the irreversibility of renormalization group flows.
  • The identified equivalence between impurity entropy and quantum relative entropy offers new insights into the dynamics of defects in conformal field theories.
  • The findings contribute to a deeper understanding of fundamental concepts in quantum field theory and statistical mechanics.