Constraint of a general effective potential in vector torsion coupled conformally induced gravity

Abstract

It is found that the deviation of an effective potential from the quartic form is related to the metric and vector torsion dependencies of the effective potential in the vector torsion coupled conformally induced gravity.

Conformally coupled induced gravity with gradient torsion

“…However, the appearance of the conformal anomaly in the conformally induced gravity is not allowed due to the constraint Eq. ( 15) which is the requirement of conformal invariance [9] from the consistency of equations of motion for the bare and the effective action in the conformally induced gravity [6]. In this reduction, the constraint which effective potential should satisfy is…”

“…It is found that induced gravity at conformal coupling should have conformal invariance for consistency [6,9]. We investigate the conformal coupling in induced gravity with a gradient torsion.…”

“…In Riemann space, the conformal coupling is unique with ξ = 1 6 . However, introducing the vector torsion, an extended conformal coupling is possible in induced gravity [5,6] because the vector torsion plays the role of a conformal gauge field in Riemann-Cartan space [3,7,8].…”

Conformal Couplings in Induced Gravity

“…Without the vector torsion, the conformally invariant induced gravity action is unique with the specific conformal coupling. However, introducing the vector torsion field, a conformally invariant extension of induced gravity action can be considered [12].…”

Effective Levi-Civita dilaton theory from Metric Affine Dilaton gravity

“…In the Tucker-Wang approach to MAG we choose the metric to be orthonormal g ab = η ab = (−1, 1, 1, 1, ...) and we vary with respect to the coframe e a and the connection ω a b considered as independent gauge potentials. As we will see the non Riemannian contribution to the Einstein-Hilbert term times ψ 2 is equivalent in the field equations to a kinetic term for the Dilaton and if no torsion terms are explicitly introduced in the action, the coupling ξ is not arbitrary contrary to what happens in Ref [5][6][7] where ξ is a free parameter. Once β is fixed we obtain an effective ξ ′ −1 given by ξ −1 + 4 n−1 n−2 (see eq.…”