Global quantum geometric Langlands at irrational level

We prove the unramified quantum geometric Langlands equivalence for every connected simple complex algebraic group G and every level $c\in \mathbb{C}\setminus \mathbb{Q}$, including non-real levels. For every smooth projective connected complex curve X, it identifies the full twisted D-module categories on ${\mathrm{Bun}}_G(X)$ and ${\mathrm{Bun}}_{G^{\vee }}(X)$ at the dual shifted levels c and $-1/(rc)$, where r is the lacing number. The equivalence uses the given global forms and includes all connected components.