Browsing by Author "Lipstein, Arthur"
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Item Cosmological Scattering Equations(2021) Gomez, Humberto; Lipinski Jusinskas, Renann; Lipstein, ArthurWe propose a world sheet formula for tree-level correlation functions describing a scalar field with arbitrary mass and quartic self-interaction in de Sitter space, which is a simple model for inflationary cosmology. The correlation functions are located on the future boundary of the spacetime and are Fourier-transformed to momentum space. Our formula is supported on mass-deformed scattering equations involving conformal generators in momentum space and reduces to the CHY formula for φ4 amplitudes in the flat space limit. Using the global residue theorem, we verify that it reproduces the Witten diagram expansion at four and six points, and sketch the extension to n points.Item Cosmological scattering equations at tree-level and one-loop(Springer Science and Business Media Deutschland GmbH, 2022-07) Gomez, Humberto; Jusinskas, Renann Lipinski; Lipstein, ArthurWe recently proposed a formula for tree-level n-point correlators of massive ϕ4 theory in de Sitter momentum space which consists of an integral over n punctures on the Riemann sphere and differential operators in the future boundary dubbed the cosmological scattering equations. This formula was explicitly checked up to six points via a map to Witten diagrams using the global residue theorem. In this work we provide further details of these calculations and present an alternative formulation based on a double cover of the Riemann sphere. This framework can be used to derive simple graphical rules for evaluating the integrals more efficiently. Using these rules, we check the validity of our formula up to eight points and sketch the derivation of n-point correlators. Finally, we propose a similar formula for 1-loop n-point correlators in terms of an integral over (n + 2) punctures on the Riemann sphere, which we verify at four points. The 1-loop formula holds for small masses in de Sitter space and arbitrary masses satisfying the Breitenlohner-Freedman bound after Wick-rotating to Anti-de Sitter space.Item New recursion relations for tree-level correlators in anti-de Sitter spacetime(2022-12-15) Armstrong, Connor; Gomez, Humberto; Lipinski Jusinskas, Renann; Lipstein, Arthur; Mei, JiajieWe present for the first time classical multiparticle solutions in anti-de Sitter space (AdS) involving scalars, gluons, and gravitons. They are recursively defined through multiparticle currents which reduce to Berends-Giele currents in the flat space limit. This construction exposes a compact definition of tree-level boundary correlators using a general prescription that removes unphysical boundary contributions. Similarly to the flat space perturbiner, a convenient gauge choice leads to a scalar basis for all degrees of freedom, while the tensor structure is exclusively captured by field theory vertices. This provides a fully automated way to compute AdS boundary correlators to any multiplicity and cosmological wave function coefficients after Wick rotating to de Sitter space.