Real Chern-Simons wave function
File(s)Real-AshKod5.pdf (218.79 KB)
Accepted version
Author(s)
Magueijo, João
Type
Journal Article
Abstract
We examine the status of the Chern-Simons (or Kodama) state from the point of view of a formulation of gravity that uses only real connection and metric variables and a real action. We may package the real connection variables into the complex self-dual Ashtekar connection (and will do so to make contact with previous work), but that operation is essentially cosmetic and can be undone at any step or even bypassed altogether. The action will remain the (real) Einstein-Cartan action, forgoing the addition of the usual Holst (or Nieh-Yan) term with an imaginary coefficient. It is then found that the constraints are solved by a modification of the Chern-Simons state which is a pure phase (in the Lorentzian theory, we stress), the phase containing only the fully gauge-invariant imaginary part of the Chern-Simons functional. Thus, the state for the “real theory” is nonpathological with regards to the most egregious criticisms facing its “nonreal” cousin, solving the complex theory. A straightforward modification of the real Chern-Simons state is also a solution in quasitopological theories based on the Euler invariant, for which the cosmological constant,
Λ
, is dynamical. In that case it is enough to shift the usual factor of
Λ
in the wave function to the inside of the spatial Chern-Simons integral. The trick only works for the quasi-Euler theory with a critical coupling previously identified in the literature. It does not apply to the quasi-Pontryagin theory.
Λ
, is dynamical. In that case it is enough to shift the usual factor of
Λ
in the wave function to the inside of the spatial Chern-Simons integral. The trick only works for the quasi-Euler theory with a critical coupling previously identified in the literature. It does not apply to the quasi-Pontryagin theory.
Date Issued
2021-07-02
Date Acceptance
2021-06-15
Citation
Physical Review D, 2021, 104 (2), pp.1-10
ISSN
2470-0010
Publisher
American Physical Society (APS)
Start Page
1
End Page
10
Journal / Book Title
Physical Review D
Volume
104
Issue
2
Copyright Statement
© 2021 American Physical Society
Sponsor
Science and Technology Facilities Council (STFC)
Science and Technology Facilities Council (STFC)
Identifier
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.104.026002
Grant Number
ST/P000762/1
ST/T000791/1
Publication Status
Published
Article Number
026002
Date Publish Online
2021-07-02