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The pure spinor formulation of superstring theory includes an interacting sector of central charge $c_{lambda}=22$, which can be realized as a curved $betagamma$ system on the cone over the orthogonal Grassmannian $text{OG}^{+}(5,10)$. We find that the spectrum of the $betagamma$ system organizes into representations of the $mathfrak{g}=mathfrak{e}_6$ affine algebra at level $-3$, whose $mathfrak{so}(10)_{-3}oplus {mathfrak u}(1)_{-4}$ subalgebra encodes the rotational and ghost symmetries of the system. As a consequence, the pure spinor partition function decomposes as a sum of affine $mathfrak{e}_6$ characters. We interpret this as an instance of a more general pattern of enhancements in curved $betagamma$ systems, which also includes the cases $mathfrak{g}=mathfrak{so}(8)$ and $mathfrak{e}_7$, corresponding to target spaces that are cones over the complex Grassmannian $text{Gr}(2,4)$ and the complex Cayley plane $mathbb{OP}^2$. We identify these curved $betagamma$ systems with the chiral algebras of certain $2d$ $(0,2)$ CFTs arising from twisted compactification of 4d $mathcal{N}=2$ SCFTs on $S^2$.
The pure spinor formulation of the ten-dimensional superstring leads to manifestly supersymmetric loop amplitudes, expressed as integrals in pure spinor superspace. This paper explores different methods to evaluate these integrals and then uses them
Mason and Skinner recently constructed a chiral infinite tension limit of the Ramond-Neveu-Schwarz superstring which was shown to compute the Cachazo-He-Yuan formulae for tree-level d=10 Yang-Mills amplitudes and the NS-NS sector of tree-level d=10 s
A covariant map between the Ramond-Neveu-Schwarz (RNS) and pure spinor formalisms for the superstring is found which transforms the RNS and pure spinor BRST operators into each other. The key ingredient is a dynamical twisting of the ten spin-half RN
We compute the massless five-point amplitude of open superstrings using the non-minimal pure spinor formalism and obtain a simple kinematic factor in pure spinor superspace, which can be viewed as the natural extension of the kinematic factor of the
The $b$-ghost of the pure spinor formalism in a general curved background is not holomorphic. For such theories, the construction of the string measure requires the knowledge of the action of diffeomorphisms on the BV phase space. We construct such a