Currents in Celestial CFT
arxiv(2024)
摘要
In this review we discuss currents in celestial CFT and the consistency of
their naive symmetry algebras. In particular we study in detail the Jacobi
identity and the double residue condition for soft insertions, hard momentum
space insertions, and hard celestial insertions. In the latter case we
introduce the notion of a "hard current" in CFT and work through examples in
the 2D critical Ising model. The current algebra of hard insertions in pure
Einstein gravity is a slight conceptual generalization of the familiar
w_1+∞-wedge current algebra. We also review branch cut terms in the
celestial OPE, which indicate new primary content and were previously missed
until recently. We work through an explicit toy example illustrating the
mechanism by which such branch cut terms can arise. These branch cut terms
prevent a symmetry interpretation but are fully compatible with a consistent
OPE.
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