  We explain how the nilpotent singular support condition introduced into the
geometric Langlands conjecture by Arinkin and Gaitsgory arises naturally from
the point of view of N = 4 supersymmetric gauge theory. We define what it means
in topological quantum field theory to restrict a category of boundary
conditions to the full subcategory of objects compatible with a fixed choice of
vacuum, both in functorial field theory and in the language of factorization
algebras. For B-twisted N = 4 gauge theory with gauge group G, the moduli space
of vacua is equivalent to h*/W , and the nilpotent singular support condition
arises by restricting to the vacuum 0 in h*/W. We then investigate the
categories obtained by restricting to points in larger strata, and conjecture
that these categories are equivalent to the geometric Langlands categories with
gauge symmetry broken to a Levi subgroup, and furthermore that by assembling
such for the groups GL_n for all positive integers n one finds a hidden
factorization structure for the geometric Langlands theory.
