Chiral Extensions of Cotangent Yangian

Abstract

We construct chiral extensions of the cotangent Yangian using vertex algebroids. At zero level, the construction yields a vertex algebra with a compatible coproduct, whose Zhu reduction recovers the cotangent Yangian of Abedin and Niu. We also construct vertex algebra extensions at non-zero levels and study level-additive coproducts. The zero-level vertex algebra admits two natural quasi-conformal structures. We compute the corresponding sphere one-point conformal blocks and equip each block space with an associative product induced by the coproduct. For the first quasi-conformal structure, the blocks space can be identified with the dual of a certain Lie algebroid homology; for the second, we describe the block algebra and its classical limit in terms of mini-twistor geometry.