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Local Quantum Energy Conditions in Non-Lorentz-Invariant Quantum Field Theories.

Daniel Grumiller1, Pulastya Parekh2,3, Max Riegler4

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This study introduces local quantum energy conditions for non-Lorentz invariant quantum field theories. These new conditions are shown to saturate for specific states in two-dimensional theories, linking to flat space holography.

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Area of Science:

  • Theoretical Physics
  • Quantum Field Theory
  • Holography

Background:

  • Local quantum energy conditions are crucial in general relativity and quantum field theory.
  • Lorentz invariance is a fundamental symmetry in standard quantum field theories.
  • Flat space holography connects quantum field theories to gravitational theories in higher dimensions.

Purpose of the Study:

  • To explore local quantum energy conditions in quantum field theories lacking Lorentz invariance.
  • To investigate theories with infinite-dimensional symmetries, such as those related to the Bondi-van der Burg-Metzner-Sachs group.
  • To establish a connection between these novel energy conditions and holographic principles.

Main Methods:

  • Development of new local quantum energy conditions tailored for non-Lorentz invariant theories.
  • Analysis of two-dimensional quantum field theories possessing infinite-dimensional symmetries.
  • Application of techniques inspired by holographic duality and the quantum null energy condition.

Main Results:

  • The first example of local quantum energy conditions for non-Lorentz invariant quantum field theories is presented.
  • These energy conditions are demonstrated to saturate for specific field theory states.
  • The saturating states are found to be dual to vacuum solutions in 3D Einstein gravity with a vanishing cosmological constant.

Conclusions:

  • The study extends the concept of quantum energy conditions to a broader class of quantum field theories.
  • The findings provide new insights into the interplay between quantum field theory and gravity in non-Lorentz invariant settings.
  • This work establishes a concrete link between novel energy conditions and holographic dualities in flat spacetimes.