Exploring 2+2 answers to 3+1 questions

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 MATHEMATICAL SCRIPT CAPITAL N?=1/2 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.

Automated summary

This article explores the potential uses of physics in Kleinian signature spacetimes (2 + 2) to understand the properties of physics in Lorentzian signature (3 + 1). Similar to how Euclidean signature quantities can be used to construct the ground state wavefunction of a Lorentzian quantum field theory, an analytic continuation to Kleinian signature can construct a low particle flux state. The existence of a natural supersymmetry algebra in 2 + 2 signature can also constrain the structure of correlation functions. The spontaneous breaking of Lorentz symmetry can produce various MATHEMATICAL SCRIPT CAPITAL N?=1/2 supersymmetry algebras in 3 + 1 signature, which correspond to nonsupersymmetric systems. Speculation is made on the possible role of these structures in addressing the cosmological constant problem.