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Journal of High Energy Physics

, 2010:41 | Cite as

Short-distance regularity of Green’s function and UV divergences in entanglement entropy

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Abstract

Reformulating our recent result (arXiv:1007.1246 [hep-th]) in coordinate space we point out that no matter how regular is short-distance behavior of Green’s function the entanglement entropy in the corresponding quantum field theory is always UV divergent. In particular, we discuss a recent example by Padmanabhan (arXiv:1007.5066 [gr-qc]) of a regular Green’s function and show that provided this function arises in a field theory the entanglement entropy in this theory is UV divergent and calculate the leading divergent term.

Keywords

Field Theories in Higher Dimensions Renormalization Regularization and Renormalons 
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References

  1. [1]
    L. Bombelli, R.K. Koul, J.H. Lee and R.D. Sorkin, A quantum source of entropy for black holes, Phys. Rev. D 34 (1986) 373 [SPIRES]. MathSciNetADSGoogle Scholar
  2. [2]
    M. Srednicki, Entropy and area, Phys. Rev. Lett. 71 (1993) 666 [hep-th/9303048] [SPIRES]. MathSciNetADSMATHCrossRefGoogle Scholar
  3. [3]
    H. Casini and M. Huerta, Entanglement entropy in free quantum field theory, J. Phys. A 42 (2009) 504007 [arXiv:0905.2562] [SPIRES].MathSciNetGoogle Scholar
  4. [4]
    T. Padmanabhan, Finite entanglement entropy from the zero-point-area of spacetime, [arXiv:1007.5066] [SPIRES].
  5. [5]
    D. Nesterov and S.N. Solodukhin, Gravitational effective action and entanglement entropy in UV modified theories with and without Lorentz symmetry, arXiv:1007.1246 [SPIRES] .
  6. [6]
    D.V. Vassilevich, Heat kernel expansion: User’s manual, Phys. Rept. 388 (2003) 279 [hep-th/0306138] [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
  7. [7]
    T. Padmanabhan, Duality and zero-point length of spacetime, Phys. Rev. Lett. 78 (1997) 1854 [hep-th/9608182] [SPIRES].ADSCrossRefGoogle Scholar

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© The Author(s) 2010

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

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques et Physique ThéoriqueUniversité François-Rabelais Tours Fédération Denis Poisson -CNRSToursFrance
  2. 2.Theory DepartmentLebedev Physical InstituteMoscowRussia

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