A specific nonminimal kinetic term for the pure tensorial component of torsion makes the gravitational couplings of quadratic gravity asymptotically free at one loop while preserving the absence of tachyons.
Functional Determinant of the Massive Laplace Operator and the Multiplicative Anomaly
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abstract
After a brief survey of zeta function regularization issues and of the related multiplicative anomaly, illustrated with a couple of basic examples, namely the harmonic oscillator and quantum field theory at finite temperature, an application of these methods to the computation of functional determinants corresponding to massive Laplacians on spheres in arbitrary dimensions is presented. Explicit formulas are provided for the Laplace operator on spheres in $N=1,2,3,4$ dimensions and for `vector' and `tensor' Laplacians on the unitary sphere $S^4$.
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Quadratic gravity with propagating torsion and asymptotic freedom
A specific nonminimal kinetic term for the pure tensorial component of torsion makes the gravitational couplings of quadratic gravity asymptotically free at one loop while preserving the absence of tachyons.