We consider the discrete
symmetry
, which takes place in the scenario of quantum gravity where the gravitational tetrads emerge as the order parameter—the vacuum expectation value of the bilinear combination of fermionic operators. Under this symmetry operation,
[...] Read more.
We consider the discrete
symmetry
, which takes place in the scenario of quantum gravity where the gravitational tetrads emerge as the order parameter—the vacuum expectation value of the bilinear combination of fermionic operators. Under this symmetry operation,
, the emerging tetrads are multiplied by the imaginary unit,
. The existence of such symmetry and the spontaneous breaking of this symmetry are also supported by the consideration of the symmetry breaking scheme in the topological superfluid
3He-B. The order parameter in
3He-B is also the bilinear combination of the fermionic operators. This order parameter is the analog of the tetrad field, but it has complex values. The
-symmetry operation changes the phase of the complex order parameter by
, which corresponds to the
discrete symmetry in quantum gravity. We also considered the alternative scenario of the breaking of this
symmetry, in which the
-operation changes sign of the scalar curvature,
, and thus the Einstein–Hilbert action violates the
-symmetry. In the alternative scenario of symmetry breaking, the gravitational coupling
plays the role of the order parameter, which changes sign under
-transformation.
Full article