Quantization of the shift of argument subalgebras in type A

Given a simple Lie algebra g and an element μ∈g⁎, the corresponding shift of argument subalgebra of S(g) is Poisson commutative. In the case where μ is regular, this subalgebra is known to admit a quantization, that is, it can be lifted to a commutative subalgebra of U(g). We show that if g is of type A, then this property extends to arbitrary μ, thus proving a conjecture of Feigin, Frenkel and Toledano Laredo. The proof relies on an explicit construction of generators of the center of the affine vertex algebra at the critical level.