Hint to Supersymmetry from GR Vacuum

Abstract

The $S$-matrix formulation of gravity suggests that the $\theta$-vacuum structure must not be sustained by the theory. We point out that, when applied to the vacuum of general relativity, this criterion hints to supersymmetry. The topological susceptibility of gravitational vacuum induced by Eguchi-Hanson instantons can be eliminated neither by spin-$1/2$ fermions nor by an axion coupled via them since such fermions do not provide instanton zero modes. Instead, the job is done by a spin-$3/2$ fermion, hence realizing a local supersymmetry. This scenario also necessitates the spontaneous breaking of supersymmetry and predicts the existence of axion of $R$-symmetry which gets mass exclusively from the gravitational instantons. The $R$-axion can be a viable dark matter candidate. Matching between the index and the anomaly imposes a constraint that spin-$1/2$ fermions should not contribute to the chiral gravitational anomaly.

arXiv comment20 pages

References in corpus (15)

• Phases of $N=2$ Theories In Two Dimensions
• Measurement of the permanent electric dipole moment of the neutron
• Black Holes and Large N Species Solution to the Hierarchy Problem
• Black Hole Bound on the Number of Species and Quantum Gravity at LHC
• Standard Model Criticality Prediction: Top mass 173 +/- 5 GeV and Higgs mass 135 +/- 9 GeV
• Quantum Compositeness of Gravity: Black Holes, AdS and Inflation
• Quantum Break-Time of de Sitter
• Small neutrino masses from gravitational $\theta$-term
• Prediction for Nonabelian Fine Structure Constants from Multicriticality
• A Simple Complete Model of Gauge-Mediated SUSY-Breaking and Dynamical Relaxation Mechanism for Solving the mu-Problem
• Gauge Couplings calculated from Multiple Point Criticality yield ${\alpha }^{-1}=136{.}_8\pm 9$: At Last the Elusive Case of $U(1)$
• Ruling Out the Massless Up-Quark Solution to the Strong CP Problem by Computing the Topological Mass Contribution with Lattice QCD
• Enhanced Instability of de Sitter Space in Einstein-Gauss-Bonnet Gravity
• Coloured gravitational instantons, the strong CP problem and the companion axion solution
• On dual formulation of Axion solution to strong-CP problem

Cited by in corpus (6)

• Lectures in Quantum Gravity
• ${\eta }_{\mathrm{w}}$-meson from topological properties of the electroweak vacuum
• Electroweak ${\eta }_{\mathrm{w}}$ meson
• A QCD R-Axion
• Vacuum energy in effective field theory of general relativity
• Consistent Canonical Quantization of Gravity: Recovery of Classical GR from BRST-invariant Coherent States