Hidden exceptional symmetry in the pure spinor superstring

The pure spinor formulation of superstring theory includes an interacting sector of central charge cλ = 22, which can be realized as a curved βγ system on the cone over the orthogonal Grassmannian OG+(5,10). We find that the spectrum of the βγ system organizes into representations of the g = e6 affine algebra at level −3, whose so(10)−3⊕u(1)−4 subalgebra encodes the rotational and ghost symmetries of the system. As a consequence, the pure spinor partition function decomposes as a sum of affine e6 characters. We interpret this as an instance of a more general pattern of enhancements in curved βγ systems, which also includes the cases g=so(8) and e7, corresponding to target spaces that are cones over the complex Grassmannian Gr(2,4) and the complex Cayley plane OP2. We identify these curved βγ systems with the chiral algebras of certain two-dimensional (2D) (0,2) conformal field theories arising from twisted compactification of 4D N = 2 superconformal field theories on S2.