Remarks on entanglement entropy for gauge fields

In gauge theories the presence of constraints can obstruct expressing the global Hilbert space as a tensor product of the Hilbert spaces corresponding to degrees of freedom localized in complementary regions. In algebraic terms, this is due to the presence of a center—a set of operators which commute with all others—in the gauge invariant operator algebra corresponding to a finite region. A unique entropy can be assigned to algebras with a center, giving a place to a local entropy in lattice gauge theories. However, ambiguities arise on the correspondence between algebras and regions. In particular, it is always possible to choose (in many different ways) local algebras with a trivial center, and hence a genuine entanglement entropy, for any region. These choices are in correspondence with maximal trees of links on the boundary, which can be interpreted as partial gauge fixings. This interpretation entails a gauge fixing dependence of the entanglement entropy. In the continuum limit, however, ambiguities in the entropy are given by terms local on the boundary of the region, in such a way relative entropy and mutual information are finite, universal, and gauge independent quantities.

Note:

26 pages, 7 figures

11.15.Ha
11.15.-q
03.65.Ud
entropy: entanglement
operator: algebra
invariance: gauge
gauge field theory
Hilbert space
gauge fixing
lattice field theory

References(29)

Figures(7)

[1]

Quantum Computation and Quantum Information

M.A. Nielsen
,
I.L. Chuang

[2]

Black hole entropy and entropy of entanglement

Daniel N. Kabat
(
- Rutgers U., Piscataway
)

- Nucl.Phys.B 453 (1995) 281-299
•
e-Print:
- hep-th/9503016
•
DOI:
- 10.1016/0550-3213(95)00443-V

[3]

Heat kernel coefficients and spectra of the vector Laplacians on spherical domains with conical singularities

Lara De Nardo
(
- Naples U. and
- INFN, Naples
)
,
Dmitri V. Fursaev
(
- Alberta U. and
- Dubna, JINR
)
,
Gennaro Miele
(
- Naples U. and
- INFN, Naples
)

- Class.Quant.Grav. 14 (1997) 1059-1078
•
e-Print:
- hep-th/9610011
•
DOI:
- 10.1088/0264-9381/14/5/013

[3]

Cones, spins and heat kernels

Dmitri V. Fursaev
(
- Alberta U. and
- Dubna, JINR
)
,
Gennaro Miele
(
- Naples U. and
- INFN, Naples
)

- Nucl.Phys.B 484 (1997) 697-723
•
e-Print:
- hep-th/9605153
•
DOI:
- 10.1016/S0550-3213(96)00631-1

[4]

Do gauge fields really contribute negatively to black hole entropy?

William Donnelly
(
- Maryland U.
)
,
Aron C. Wall
(
- UC, Santa Barbara
)

- Phys.Rev.D 86 (2012) 064042
•
e-Print:
- 1206.5831
•
DOI:
- 10.1103/PhysRevD.86.064042

[5]

Entanglement entropy of black holes

Sergey N. Solodukhin
(
- Tours U., CNRS
)

- Living Rev.Rel. 14 (2011) 8
•
e-Print:
- 1104.3712
•
DOI:
- 10.12942/lrr-2011-8

[5]

Remarks on effective action and entanglement entropy of Maxwell field in generic gauge

Sergey N. Solodukhin
(
- Fed. Denis Poisson, Tours and
- Santa Barbara, KITP
)

- JHEP 12 (2012) 036
•
e-Print:
- 1209.2677
•
DOI:
- 10.1007/JHEP12(2012)036

[6]

Entropy, Contact Interaction with Horizon and Dark Energy

Ariel R. Zhitnitsky
(
- British Columbia U.
)

- Phys.Rev.D 84 (2011) 124008
•
e-Print:
- 1105.6088
•
DOI:
- 10.1103/PhysRevD.84.124008

[7]

Kabat's surface terms in the zeta function approach

D. Iellici
(
- Trento U. and
- INFN, Trento
)
,
V. Moretti
(
- Trento U. and
- INFN, Trento
)

•
e-Print:
- hep-th/9703088

[8]

Entanglement entropy for even spheres

J.S. Dowker
(
- Manchester U.
)

e-Print:
- 1009.3854

[9]

Entanglement and Thermal Entropy of Gauge Fields

Christopher Eling
(
- Potsdam, Max Planck Inst.
)
,
Yaron Oz
(
- Tel Aviv U.
)
,
Stefan Theisen
(
- Potsdam, Max Planck Inst.
)

- JHEP 11 (2013) 019
•
e-Print:
- 1308.4964
•
DOI:
- 10.1007/JHEP11(2013)019

[10]

Disk entanglement entropy for a Maxwell field

- Phys.Rev.D 89 (2014) 2, 025018
•
e-Print:
- 1310.4886
•
DOI:
- 10.1103/PhysRevD.89.025018

[11]

Entanglement entropy in gauge theories and the holographic principle for electric strings

P.V. Buividovich
(
- Joint Inst. Power Nucl. Res., Minsk and
- Moscow, ITEP
)
,
M.I. Polikarpov
(
- Moscow, ITEP
)

- Phys.Lett.B 670 (2008) 141-145
•
e-Print:
- 0806.3376
•
DOI:
- 10.1016/j.physletb.2008.10.032

[12]

Decomposition of entanglement entropy in lattice gauge theory

William Donnelly
(
- Maryland U.
)

- Phys.Rev.D 85 (2012) 085004
•
e-Print:
- 1109.0036
•
DOI:
- 10.1103/PhysRevD.85.085004

[13]

Hamiltonian Formulation of Wilson's Lattice Gauge Theories

John B. Kogut
(
- Cornell U., LNS
)
,
Leonard Susskind
(
- Yeshiva U. and
- Tel Aviv U. and
- Cornell U., LNS
)

- Phys.Rev.D 11 (1975) 395-408
•
DOI:
- 10.1103/PhysRevD.11.395

[13]

Gauge Fields on a Lattice. 1. General Outlook

- Phys.Rev.D 10 (1974) 3376,
- In *Rebbi, C. ( Ed.): Lattice Gauge Theories and Monte Carlo Simulations*, 74-93. ( Phys. Rev. D10 ( 1974) 3376-3395) and Saclay Cen - D.PH.T-74-038 (74,REC.JUN.) 53p
•
DOI:
- 10.1103/PhysRevD.10.3376