Conformal Invariance in Einstein–cartan–weyl Space

Abstract

We consider conformally invariant form of the actions in Einstein, Weyl, Einstein-Cartan and Einstein-Cartan-Weyl space in general dimensions(> 2) and investigate the relations among them. In Weyl space, the observational consistency condition for the vector field determining non-metricity of the connection can be obtained from the equation of motion. In Einstein-Cartan space a similar role is played by the vector part of the torsion tensor. We consider the case where the trace part of the torsion is the Kalb-Ramond type of field. In this case, we express conformally invariant action in terms of two scalar fields of conformal weight −1, which can be cast into some interesting form. We discuss some applications of the result.

Supersymmetric near-horizon geometry and Einstein-Cartan-Weyl spaces

“…where ξ denotes an arbitrary parameter that we are free to include [41,42]. This means that the torsion and the nonmetricity tensor transform respectively as…”

“…One can now use the expression (30) for the Ricci scalar of the affine connection to rephrase the constraint (43) as (62). Finally, using (43), we see that (42) is equivalent to the ECW equations (63), that is the set of partial differential equations characterizing an Einstein-Cartan-Weyl manifold in the gauge (41), subject to the conditions (37) and (62), together with the constraints on the trace part of the torsion (cf. (46) and (47)) and on the traceless part of the distortion (cf.…”

Quantum treatment of the Weyl vector meson

“…Here we shall consider the specific model with only one scalar field multiplet, displayed in Eq. (26). In general, there might be other scalar fields present, in which case the solution discussed below may be suitably generalized.…”

“…It was later revived by many authors [8][9][10][11][12][13][14][15][16]. Subsequently local scale invariance has attracted considerable attention in literature [17][18][19][20][21][22][23][24][25][26]. It has been shown that a scale-invariant model of gravity is equivalent to the Einstein's action with an effective gravitational constant [27].…”

Space-time singularities in Weyl manifolds

“…It is our purpose here to pursue this question further in the light of some modified gravity theories formulated in a particular kind of space-time geometry, namely, the so-called Weyl integrable space-time (WIST) [17][18][19][20][21][22][23][24][25][26][27][28][29].…”