No-boundary state for Klein space

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Abstract
Analytic continuation from (3, 1) signature Minkowski to (2, 2) signature Klein space has emerged as a useful tool for the understanding of scattering amplitudes and flat space holography. Under this continuation, past and future null infinity merge into a single boundary ( J ) which is the product of a null line with a (1, 1) signature torus. The Minkowskian S -matrix continues to a Kleinian S -vector which in turn may be represented by a Poincaré-invariant vacuum state | C ⟩ in the Hilbert space built on J . | C ⟩ contains all information about S in a novel, repackaged form. We give an explicit construction of | C ⟩ in a Lorentz/conformal basis for a free massless scalar. J separates into two halves J ± which are the asymptotic null boundaries of the regions timelike and spacelike separated from the origin. | C ⟩ is shown to be a maximally entangled state in the product of the J ± Hilbert spaces.
Funding Information
  • John Templeton Foundation (Black Hole Initiative)
  • National Science Foundation (NSF PHY-2207659)
  • Simons Foundation (Simons Collaboration on Celestial Holography)
  • Gordon and Betty Moore Foundation (Black Hole Initiative)

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