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Relative entropy and proximity of quantum field theories

  • Vijay Balasubramanian
  • Jonathan J. Heckman
  • Alexander Maloney
Open Access
Regular Article - Theoretical Physics

Abstract

We study the question of how reliably one can distinguish two quantum field theories (QFTs). Each QFT defines a probability distribution on the space of fields. The relative entropy provides a notion of proximity between these distributions and quantifies the number of measurements required to distinguish between them. In the case of nearby conformal field theories, this reduces to the Zamolodchikov metric on the space of couplings. Our formulation quantifies the information lost under renormalization group flow from the UV to the IR and leads us to a quantification of fine-tuning. This formalism also leads us to a criterion for distinguishability of low energy effective field theories generated by the string theory landscape.

Keywords

Conformal and W Symmetry Statistical Methods Renormalization Group 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Vijay Balasubramanian
    • 1
    • 2
    • 3
  • Jonathan J. Heckman
    • 4
  • Alexander Maloney
    • 5
  1. 1.David Rittenhouse LaboratoriesUniversity of PennsylvaniaPhiladelphiaU.S.A.
  2. 2.CUNY Graduate Center, Initiative for the Theoretical SciencesNew YorkU.S.A.
  3. 3.Theoretische Natuurkunde, Vrije Universiteit Brussel, and International Solvay InstitutesBrusselsBelgium
  4. 4.Department of PhysicsUniversity of North Carolina at Chapel HillChapel HillU.S.A.
  5. 5.Department of PhysicsMcGill UniversityMontrealCanada

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