We prove that the ind-scheme ? consisting of regular maps from an affine curve to a simple, simply-connected group G as closed points is an irreducible and reduced ind-projective variety. By taking the Laurent series expansion at any point at infinity, we can view ? as a subgroup of the loop group. We prove that the central extension of the loop group splits over ? if the affine curve has a single point at infinity. We prove that the space of vacua for any s-pointed smooth curve ? is identified with the space of global sections of the moduli stack of quasi-parabolic G-bundles over ? with respect to a certain line bundle. We also determine the Picard group of this moduli stack. We introduce the notion of theta bundle for a family of G-bundles over ? and determine it for the tautological family of G-bundles over ? parameterized by the infinite Grassmannian in terms of the Dynkin index. The main result of this chapter asserts that there is a canonical identification between the space of global sections of a line bundle over the coarse moduli space of parabolic G-bundles over any s-pointed smooth projective curve ? and the space of vacua.