Monday, April 1, 2019

Conformal Gravity v. SUSY and String Theory With Higgs Insights

Mannheim plays for more than just gravity, arguing for an alternative solution to the so called "hierarchy problem" and making the case that supersymmetry (SUSY) and string theory aren't necessary after all.

Living Without Supersymmetry -- the Conformal Alternative and a Dynamical Higgs Boson

We show that key results of supersymmetry can be achieved via conformal symmetry. We propose that the Higgs boson be a dynamical bound state rather than an elementary scalar, so that there is no quadratic divergence self-energy problem for it and no need to invoke supersymmetry to resolve it. We study a conformal invariant theory of interacting fermions and gauge bosons, in which there is scaling with anomalous dimensions and dynamical symmetry breaking, with the dynamical dimension of ψ¯ψ being reduced from 3 to 2. With this reduction we augment the theory with a then renormalizable 4-fermion interaction with dynamical dimension equal to 4. We reinterpret the theory as a renormalizable version of the Nambu-Jona-Lasinio (NJL) model, with the gauge theory sector with its now massive fermion being the mean field and the 4-fermion interaction being the residual interaction. It is this residual interaction that generates dynamical Goldstone and Higgs states, states that, as noted by Baker and Johnson, the gauge theory sector itself does not possess. The Higgs boson is found to be a narrow resonance just above threshold. We couple the theory to conformal gravity, with the interplay between conformal gravity and the 4-fermion interaction taking care of the vacuum energy problem. With conformal gravity being a consistent quantum gravity theory there is no need for string theory with its supersymmetric underpinnings. With conformal gravity fits to galactic rotation curves and the accelerating universe not needing dark matter, there is no need to introduce supersymmetry for either the vacuum energy problem or to provide a potential dark matter candidate. We propose that it is conformal symmetry rather than supersymmetry that is fundamental, with the theory of nature being a locally conformal, locally gauge invariant, non-Abelian NJL theory.
Comments:53 pages, 12 figures. Added section on the all-order renormalizability of the four-fermion interaction
Subjects:High Energy Physics - Phenomenology (hep-ph); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Cite as:arXiv:1506.01399 [hep-ph]
 (or arXiv:1506.01399v4 [hep-ph] for this version)


neo said...

LHC data is consistent with a standard SM fundamental scalar which is at odds with this paper.

andrew said...

Not sure that there is a distinguishable difference between a fundamental scalar and a composite one with the same properties in existing LHC data.

neo said...

how does Philip D. Mannheim proposal differ from already existing large literature on composite higgs, which proposes a new force in analogy to QCD binding a new set of fermions? these models make falsifiable predictions that LHC should find, but, like SUSY, haven't.