Hint to supersymmetry from the GR vacuum

The <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>S</a:mi></a:math>-matrix formulation of gravity suggests that the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>θ</c:mi></c:math>-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-<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mn>1</e:mn><e:mo>/</e:mo><e:mn>2</e:mn></e:math> 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-<g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mn>3</g:mn><g:mo>/</g:mo><g:mn>2</g:mn></g:math> fermion, hence realizing a local supersymmetry. This scenario also necessitates the spontaneous breaking of supersymmetry and predicts the existence of axion of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>R</i:mi></i:math> symmetry which gets mass exclusively from the gravitational instantons. The <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>R</k:mi></k:math> axion can be a viable dark matter candidate. Matching between the index and the anomaly imposes a constraint that spin-<m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mn>1</m:mn><m:mo>/</m:mo><m:mn>2</m:mn></m:math> fermions should not contribute to the chiral gravitational anomaly. Published by the American Physical Society 2024