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Description
First developed for the conformal bootstrap, weight-shifting operators have long been used to perform integer-shifts in scaling dimension of correlators of conformal primaries. These weight-shifting operators are differential operators that act on pairs of fields, and have been applied to compute wavefunction coefficients on the future boundary of de Sitter space from more simple 'seed functions'. In a recent paper titled 'Cosmological Weight-Shifting Matrices', myself and my co-authors show that, when acting on a set of master integrals for a given wavefunction coefficient, the action of weight-shifting operators can be re-cast as simple matrix multiplication. Our matrices shift the scaling dimensions of individual fields by an integer. They can thus be applied to a broader range of problems and are simpler to implement than earlier derivative-based approaches. By introducing a Kronecker product representation of our matrix formulation, we generalise weight-shifting operators beyond four-point functions to arbitrary tree-level diagrams. Our construction provides a systematic and graph-local approach to generating cosmologically relevant correlators from simpler master integrals.