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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 ( ) which is the product of a null line with a (1, 1) signature torus. The Minkowskian -matrix continues to a Kleinian -vector which in turn may be represented by a Poincaré-invariant vacuum state in the Hilbert space built on . contains all information about in a novel, repackaged form. We give an explicit construction of in a Lorentz/conformal basis for a free massless scalar. separates into two halves which are the asymptotic null boundaries of the regions timelike and spacelike separated from the origin. is shown to be a maximally entangled state in the product of the Hilbert spaces.more » « lessFree, publicly-accessible full text available April 17, 2026
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Melton, Walker; Narayanan, Sruthi A; Strominger, Andrew (, Journal of High Energy Physics)A<sc>bstract</sc> Symmetry algebras deriving from towers of soft theorems can be deformed by a short list of higher-dimension Wilsonian corrections to the effective action. We study the simplest of these deformations in gauge theory arising from a massless complex scalar coupled toF2. The soft gauge symmetry ‘s-algebra’, compactly realized as a higher-spin current algebra acting on the celestial sphere, is deformed and enlarged to an associative algebra containing soft scalar generators. This deformed soft algebra is found to be non-abelian even in abelian gauge theory. A two-parameter family of central extensions of thes-subalgebra are generated by shifting and decoupling the scalar generators. It is shown that these central extensions can also be generated by expanding around a certain non-trivial but Lorentz invariant shockwave type background for the scalar field.more » « less
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