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Novel edge states in self-dual gravity

  • A. P. Balachandran
  • Amilcar R. de Queiroz
  • M. Arshad Momen
Open Access
Regular Article - Theoretical Physics

Abstract

In contrast to the Einstein-Hilbert action, the action for self-dual gravity contains vierbeins. They are eleminated at the level of observables by an SL(2, ℂ) gauge condition implied by the action. We argue that despite this condition, new “edge” or superselected state vectors corresponding to maps of the spheres S 2 at infinity to SL(2, ℂ) arise. They are characterised by new quantum numbers and they lead to mixed states. For black holes, they arise both at the horizon and the spatial infinity and may be relevant for the black hole information paradox. Similar comments can be made about the EinsteinPalatini action which uses vierbeins.

Keywords

Gauge Symmetry Classical Theories of Gravity 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    J.F. Carinena, A. Ibort, G. Marmo and G. Morandi, Geometry from Dynamics, Classical and Quantum, Springer (2015).Google Scholar
  2. [2]
    A.P. Balachandran, T.R. Govindarajan and B. Vijayalakshmi, Particles of Half Integral or Integral Helicity by Quantization of a Nonrelativistic Free Particle and Related Topics, Phys. Rev. D 18 (1978) 1950 [INSPIRE].
  3. [3]
    A.P. Balachandran, L. Chandar and A. Momen, Edge states in gravity and black hole physics, Nucl. Phys. B 461 (1996) 581 [gr-qc/9412019] [INSPIRE].
  4. [4]
    A. Momen, Edge dynamics for BF theories and gravity, Phys. Lett. B 394 (1997) 269 [hep-th/9609226] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    A.P. Balachandran, A.R. de Queiroz and S. Vaidya, Entropy of Quantum States: Ambiguities, Eur. Phys. J. Plus 128 (2013) 112 [arXiv:1212.1239] [INSPIRE].CrossRefGoogle Scholar
  6. [6]
    A.P. Balachandran, A.R. de Queiroz and S. Vaidya, Quantum Entropic Ambiguities: Ethylene, Phys. Rev. D 88 (2013) 025001 [arXiv:1302.4924] [INSPIRE].
  7. [7]
    A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448 [INSPIRE].
  8. [8]
    P.A.M. Dirac, Gauge invariant formulation of quantum electrodynamics, Can. J. Phys. 33 (1955) 650 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    S. Mandelstam, Quantum electrodynamics without potentials, Annals Phys. 19 (1962) 1 [INSPIRE].ADSCrossRefMATHGoogle Scholar
  10. [10]
    A.P. Balachandran and S. Vaidya, Spontaneous Lorentz violation in gauge theories, Eur. Phys. J. Plus 128 (2013) 118.CrossRefGoogle Scholar
  11. [11]
    A.P. Balachandran, S. KürkçüoǦlu, A.R. de Queiroz and S. Vaidya, Spontaneous Lorentz Violation: The Case of Infrared QED, Eur. Phys. J. C 75 (2015) 89 [arXiv:1406.5845] [INSPIRE].
  12. [12]
    A.P. Balachandran, QCD Breaks Lorentz Invariance and Colour, Mod. Phys. Lett. A 31 (2016) 1650060 [arXiv:1509.05235] [INSPIRE].
  13. [13]
    A.P. Balachandran and V.P. Nair, An Action for the Infrared Regime of Gauge Theories and the Problem of Color Transformations, arXiv:1804.07214 [INSPIRE].
  14. [14]
    A. Ashtekar and R. Tate. Lectures on Non-Perturbative Canonical Gravity, World Scientific (1991).Google Scholar
  15. [15]
    A. Ashtekar, A.P. Balachandran and S. Jo, The CP Problem in Quantum Gravity, Int. J. Mod. Phys. A 4 (1989) 1493 [INSPIRE].
  16. [16]
    M. Geiller, Lorentz-diffeomorphism edge modes in 3d gravity, JHEP 02 (2018) 029 [arXiv:1712.05269] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • A. P. Balachandran
    • 1
  • Amilcar R. de Queiroz
    • 2
  • M. Arshad Momen
    • 3
  1. 1.Physics DepartmentSyracuse UniversitySyracuseU.S.A.
  2. 2.Instituto de FisicaUniversidade de BrasiliaBrasiliaBrazil
  3. 3.Department of Physical SciencesIndependent UniversityDhakaBangladesh

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