The real Chern-Simons wave function

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 {\it 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 non-pathological with regards to the most egregious criticisms facing its "non-real" cousin, solving the complex theory. A straightforward modification of the real Chern-Simons state is also a solution in quasi-topological theories based on the Euler invariant, for which the cosmological constant, $\Lambda$, is dynamical. In that case it is enough to shift the usual factor of $\Lambda$ 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.

Version accepted for publication

References in corpus (8)

• Quantum Gravity at a Lifshitz Point
• Quantum gravity with a positive cosmological constant
• Barbero-Immirzi field in canonical formalism of pure gravity
• From the Einstein-Cartan to the Ashtekar-Barbero canonical constraints, passing through the Nieh-Yan functional
• A Note On The Chern-Simons And Kodama Wavefunctions
• Quantum cosmology of a dynamical Lambda
• A generalized Hartle-Hawking wavefunction
• Quantum torsion and a Hartle-Hawking "beam''

Cited by in corpus (10)

• Cauchy Slice Holography: A New AdS/CFT Dictionary
• An Inner Product for 4D Quantum Gravity and the Chern-Simons-Kodama State
• Minisuperspace Quantum Cosmology from the Einstein-Cartan Path Integral
• Quantum cosmology of pure connection general relativity
• Semiclassical limit problems with concurrent use of several clocks in quantum cosmology
• Unimodular Hartle-Hawking wave packets and their probability interpretation
• Lorentzian quantum cosmology with torsion
• Lower bound on the cosmological constant from the classicality of the Early Universe
• Torsion and the Probability of Inflation
• Linking the Baum-Hawking-Coleman Mechanism with Unimodular Gravity and Vilenkin's Probability Flux