  Certain deformable families of vertex algebras acquire at a limit of the
deformation parameter a large center, similar to affine Lie algebras at
critical level. Then the vertex algebra and its representation category become
a bundle over the variety defined by this large center. The zero-fibre becomes
a vertex algebra, the other fibres become twisted modules over this vertex
algebra.
  We explore these ideas and a conjectural correspondence in a class of vertex
algebras $A^{(p)}[\mathfrak{g},\kappa]$ associated to a choice of a
finite-dimensional semisimple Lie algebra and an integer $(\mathfrak{g},p)$ and
a level $\kappa$, and some related algebras. These algebras were introduced
under the name quantum geometric Langlands kernels and have an interpretation
in 4-dimensional quantum field theory. In the limit $\kappa\to \infty$, they
acquire a large central subalgebra identified with the ring of functions on the
space of $\mathfrak{g}$-connections. The zero-fibre is expected to be the
Feigin-Tipunin algebra $W_p(\mathfrak{g})$, whose category of representations
is expected to be equivalent to the small quantum group by the logarithmic
Kazhdan Lusztig conjecture.
  Our rigorous results focus on the cases $(\mathfrak{g},1)$ and
$(\mathfrak{sl}_2,2)$. In the first part of the paper, which might be of
independent interest, we discuss the twisted modules (including twists by
unipotent elements) of the affine Lie algebra and of the triplet algebra
$W_2(\mathfrak{sl}_2)$, and introduce a method of twisted free field
realization to obtain twisted modules for arbitrary $(\mathfrak{g},p)$. We also
match our findings to the respective quantum group with big center. In the
second part of the paper we match the results to the vertex algebra bundle we
compute from the limit of $A^{(p)}[\mathfrak{g},\kappa]$, which in our cases
have realizations as GKO coset resp. N=4 superconformal algebras.
