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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 Formula: see text supersymmetry algebras that in 3 + 1 signature correspond to nonsupersymmetric systems. We speculate on the possible role of these structures in addressing the cosmological constant problem.
Heckman et al. (Sun,) studied this question.
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