Proof of the quantum null energy condition for free fermionic field theories

Oct 16, 2019
13 pages
Published in:
  • Phys.Rev.D 101 (2020) 6, 066028
  • Published: Mar 26, 2020
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Abstract: (APS)
The quantum null energy condition (QNEC) is a quantum generalization of the null energy condition, which gives a lower bound on the null energy in terms of the second derivative of the von Neumann entropy or entanglement entropy of some region with respect to a null direction. The QNEC states that ⟨Tkk⟩p≥limA→0(ℏ2πASout′′), where Sout is the entanglement entropy restricted to one side of a codimension-2 surface Σ, which is deformed in the null direction about a neighborhood of point p with area A. A proof of QNEC has been given before, which applies to free and super-renormalizable bosonic field theories, and to any points that lie on a stationary null surface. Using similar assumptions and methods, we prove the QNEC for fermionic field theories.
Note:
  • 13 pages, 3 figures
  • String theory
  • quantum gravity
  • gauge/gravity duality
  • fermion: field theory
  • entropy: entanglement
  • entropy: von Neumann
  • boson: field theory
  • gauge field theory: boson
  • null-energy condition
  • surface