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arXiv · 2208.02267

Exploring $\boldsymbol{2+2}$ Answers to $\boldsymbol{3+1}$ Questions

Jonathan J. Heckman·Austin Joyce·Jeremy Sakstein·Mark Trodden
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Abstract

We explore potential uses of physics formulated in Kleinian (i.e., $2+2$) signature spacetimes as a tool for understanding properties of physics in Lorentzian (i.e., $3+1$) signature. Much as Euclidean (i.e., $4+0$) signature quantities can be used to formally construct the ground state wavefunction of a Lorentzian signature quantum field theory, a similar analytic continuation to Kleinian signature constructs a state of low particle flux in the direction of analytic continuation. There is also a natural supersymmetry algebra available in $2+2$ signature, which serves to constrain the structure of correlation functions. Spontaneous breaking of Lorentz symmetry can produce various $\mathcal{N} = 1/2$ supersymmetry algebras that in $3 + 1$ signature correspond to non-supersymmetric systems. We speculate on the possible role of these structures in addressing the cosmological constant problem.

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Jonathan J. Heckman, Austin Joyce, Jeremy Sakstein, Mark Trodden. 2022-12-30. Exploring $\boldsymbol{2+2}$ Answers to $\boldsymbol{3+1}$ Questions. https://arxiv.org/abs/2208.02267

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