Abstract
We study fermionic bulk fields in the dS/CFT dualities relating mathcal{N} = 2 su- persymmetric Euclidean vector models with reversed spin-statistics in three dimensions to supersymmetric Vasiliev theories in four-dimensional de Sitter space. These dualities specify the Hartle-Hawking wave function in terms of the partition function of deforma- tions of the vector models. We evaluate this wave function in homogeneous minisuperspace models consisting of supersymmetry-breaking combinations of a half-integer spin field with either a scalar, a pseudoscalar or a metric squashing. The wave function appears to be well-behaved and globally peaked at or near the supersymmetric de Sitter vacuum, with a low amplitude for large deformations. Its behavior in the semiclassical limit qualitatively agrees with earlier bulk computations both for massless and massive fermionic fields.
Highlights
An interesting point in this respect is that in dS/CFT the Euclidean duals are never Wick rotated to the Lorentzian
We study fermionic bulk fields in the dS/CFT dualities relating N = 2 supersymmetric Euclidean vector models with reversed spin-statistics in three dimensions to supersymmetric Vasiliev theories in four-dimensional de Sitter space
These dualities specify the Hartle-Hawking wave function in terms of the partition function of deformations of the vector models. We evaluate this wave function in homogeneous minisuperspace models consisting of supersymmetry-breaking combinations of a half-integer spin field with either a scalar, a pseudoscalar or a metric squashing
Summary
As we have described in [22], half-integer spin CFT sources enter into the Hartle-Hawking wave function and the duality eq (1.1) in a way that is formally completely analogous to the bulk bosons. If the negative frequency modes had entered as well, we would have got variables with nontrivial anticommutation relations It is clear how, for example, we should interpret the J1/2 source of the boundary CFT related to a spin-1/2 bulk field, which enters into the wave function as Grassmann valued spinors, rather than fully quantised fermionic fields. The Ψi1···ik only depend on the bosonic fields and the inner product between two bulk wave functions is given by (Ψ, Φ) = (ΨBosonic, ΦBosonic)B + (Ψ0, Φ0)B + (Ψ00, Φ00)B + (Ψ1, Φ1)B + (Ψ01, Φ01)B + (Ψ001, Φ001)B + . Here we are normalising against the value of the wave function at the given bosonic deformation B This means that we effectively consider the wavefunction of a state where we have already fixed bosonic fields to a certain value. It is clear from the form of eq (2.5) that e.g. < λ >= 0
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