Towards spacetime entanglement entropy for interacting theories

被引:21
作者
Chen, Yangang [1 ]
Hackl, Lucas [2 ]
Kunjwal, Ravi [3 ,4 ]
Moradi, Heidar [5 ,6 ]
Yazdi, Yasaman K. [7 ,8 ]
Zilhao, Miguel [9 ]
机构
[1] Univ Waterloo, Dept Appl Math, 200 Univ Ave West, Waterloo, ON N2L 3G1, Canada
[2] Univ Copenhagen, Dept Math Sci, QMATH, Univ Pk 5, DK-2100 Copenhagen, Denmark
[3] Perimeter Inst Theoret Phys, 31 Caroline St N, Waterloo, ON N2L 2Y5, Canada
[4] Univ Libre Bruxelles, Ecole Polytech Bruxelles, Ctr Quantum Informat & Commun, CP 165, B-1050 Brussels, Belgium
[5] Ctr Math Sci, Dept Appl Math & Theoret Phys, Wilberforce Rd, Cambridge CB3 0WA, England
[6] Dept Phys, Cavendish Lab, 19 JJ Thomson Ave, Cambridge CB3 0HE, England
[7] Univ Alberta, Dept Phys, 4-181 CCIS, Edmonton, AB T6G 2E1, Canada
[8] Imperial Coll London, Blackett Lab, Theoret Phys Grp, London SW7 2AZ, England
[9] Univ Lisbon, Inst Super Tecn, Dept Fis, CENTRA, Ave Rovisco Pais 1, P-1049 Lisbon, Portugal
关键词
Black Holes; Models of Quantum Gravity; QUANTUM; FIELDS;
D O I
10.1007/JHEP11(2020)114
中图分类号
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号
摘要
Entanglement entropy of quantum fields in gravitational settings is a topic of growing importance. This entropy of entanglement is conventionally computed relative to Cauchy hypersurfaces where it is possible via a partial tracing to associate a reduced density matrix to the spacelike region of interest. In recent years Sorkin has proposed an alternative, manifestly covariant, formulation of entropy in terms of the spacetime two-point correlation function. This formulation, developed for a Gaussian scalar field theory, is explicitly spacetime in nature and evades some of the possible non-covariance issues faced by the conventional formulation. In this paper we take the first steps towards extending Sorkin's entropy to non-Gaussian theories where Wick's theorem no longer holds and one would expect higher correlators to contribute. We consider quartic perturbations away from the Gaussian case and find that to first order in perturbation theory, the entropy formula derived by Sorkin continues to hold but with the two-point correlators replaced by their perturbation-corrected counterparts. We then show that our results continue to hold for arbitrary perturbations (of both bosonic and fermionic theories). This is a non-trivial and, to our knowledge, novel result. Furthermore we also derive closed-form formulas of the entanglement entropy for arbitrary perturbations at first and second order. Our work also suggests avenues for further extensions to generic interacting theories.
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页数:32
相关论文
共 53 条
[1]  
[Anonymous], 2016, PRINCETON LANDMARKS
[2]  
[Anonymous], 1965, Commun. Math. Phys.
[3]   A preferred ground state for the scalar field in de Sitter space [J].
Aslanbeigi, S. ;
Buck, M. .
JOURNAL OF HIGH ENERGY PHYSICS, 2013, (08)
[4]  
Bär C, 2009, LECT NOTES PHYS, V786, P1, DOI 10.1007/978-3-642-02780-2_1
[5]   Horizon molecules in causal set theory [J].
Barton, Christopher ;
Counsell, Andrew ;
Dowker, Fay ;
Gould, Dewi S. W. ;
Taylor, Gwylim ;
Jubb, Ian .
PHYSICAL REVIEW D, 2019, 100 (12)
[6]   WHEN IS A FIELD-THEORY A GENERALIZED FREE FIELD [J].
BAUMANN, K .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1975, 43 (03) :221-223
[7]   Thermodynamical Property of Entanglement Entropy for Excited States [J].
Bhattacharya, Jyotirmoy ;
Nozaki, Masahiro ;
Takayanagi, Tadashi ;
Ugajin, Tomonori .
PHYSICAL REVIEW LETTERS, 2013, 110 (09)
[8]   Entanglement entropy of squeezed vacua on a lattice [J].
Bianchi, Eugenio ;
Hackl, Lucas ;
Yokomizo, Nelson .
PHYSICAL REVIEW D, 2015, 92 (08)
[9]   Relative entropy and holography [J].
Blanco, David D. ;
Casini, Horacio ;
Hung, Ling-Yan ;
Myers, Robert C. .
JOURNAL OF HIGH ENERGY PHYSICS, 2013, (08)
[10]   QUANTUM SOURCE OF ENTROPY FOR BLACK-HOLES [J].
BOMBELLI, L ;
KOUL, RK ;
LEE, J ;
SORKIN, RD .
PHYSICAL REVIEW D, 1986, 34 (02) :373-383