Power-counting renormalizable, ghost-and-tachyon-free Poincaré gauge theories

Abstract

We present 48 further examples, in addition to the 10 identified in [1], of ghost-and-tachyon-free critical cases of parity-conserving Poincaré gauge theories of gravity (PGT + ) that are also powercounting renormalizable (PCR). This is achieved by extending the range of critical cases considered. Of the new PCR theories, 7 have 2 massless degrees of freedom (d.o.f.) in propagating modes and a massive 0 − or 2 − mode, 8 have only 2 massless d.o.f., and 33 have only massive mode(s). We also clarify the treatment of non-propagating modes in determining whether a theory is PCR. *

Ghost and Tachyon Free Propagation up to spin-3 in Lorentz Invariant Field Theories

“…In this section we will extensively revisit Proca and Stueckelberg theories and will follow the analysis with a slightly unorthodox look towards the mechanism of spontaneous symmetry breaking. This subject has been already exposed in [27], but we find necessary to present it here as well, before moving to more complex scenarios. We start analyzing the massive vector system described by the Proca action…”

Radiatively stable ghost and tachyon freedom in Metric Affine Gravity

“…T α µ ν and Q ρµν are linked, respectively, to the geometrical properties of torsion and non-metricity, and aid to easily distinguish different classes of theories when one, or both of them, is set to zero. The resulting model, sometimes in the related form of Poincaré gauge theory, has been lengthily studied [10][11][12][13][14][15][16][17][18][19][20][27][28][29][30][31][32][33]. We relies, in particular, to the form of the 28 parameters MAG action presented in [21], which we reproduce here unadulterated 13)µν c 7 F (13) µν + c 8 F (13) νµ + F (14)µν c 9 F (14) µν + c 10 F (14) νµ + +F (14)µν c 11 F (13) µν + c 12 F (13) νµ + F µν c 13 F µν + c 14 F (13) µν + c 15 F (14) µν…”

“…Indeed, the success of Yang-Mills and Einstein-Hilbert theories appear to indirectly support the relevance of ghost-and tachyon-freedom, as shown in [10,[37][38][39][40]. Considering MAG, extensive literature has been produced to identify sectors of the large parameter space that allow a healthy propagation of additional particles [11][12][13][14][15][16][17][18][19][20][21]. The presence of high-rank fields, carriers of multiple particle states, brings to this search an intrinsic complexity 1 .…”

Nonlinear Hamiltonian analysis of new quadratic torsion theories Part I. Cases with curvature-free constraints

“…unitary theories [4,5]. An exhaustive survey by Lin, Hobson, and Lasenby [6,7] recently found that there are 450 unitary cases in total. Of these, 58 are also power-counting renormalisable (PCR), such that the graviton and roton propagators tend to p −4 and p −2 respectively in the ultraviolet limit 2 .…”

“…By implementing the algorithm of Dirac and Bergmann, we are guaranteed to obtain all propagating degrees of freedom (D.o.F), along with all constraints [14]. In the linearised theory, this is especially easy, and allows us to verify the particle spectra and unitarity of the cases obtained in [6,7]. In the nonlinear case, the algorithm allows us to flag potentially fatal pathologies which develop under significant departures from Minkowski spacetime -if this spacetime is taken to be a vacuum, then the nonlinear regime is equivalent to that of strong fields.…”