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Register a new userDynamical twisting and the b ghost in the pure spinor formalism
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Authors
Nathan Berkovits
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After adding an RNS-like fermionic vector psi^m to the pure spinor formalism, the non-minimal b ghost takes a simple form similar to the pure spinor BRST operator. The N=2 superconformal field theory generated by the b ghost and the BRST current can be interpreted as a dynamical twisting of the RNS formalism where the choice of which spin half psi^m variables are twisted into spin 0 and spin 1 variables is determined by the pure spinor variables that parameterize the coset SO(10)/U(5).
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In the pure spinor formalism for the superstring, the b-ghost is a composite operator satisfying {Q,b}=T where Q is the pure spinor BRST operator and T is the holomorphic stress tensor. The b-ghost is holomorphic in a flat target-space background, but it is not holomorphic in a generic curved target-space background and instead satisfies $barpartial b$ = [Q, Omega] for some Omega. In this paper, Omega is explicitly constructed for the case of an open superstring in a super-Maxwell background.
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
to calculate the kinematic factors of the one-loop and two-loop massless four-point amplitudes involving two and four Ramond states.
It is well known in NSR string theory, that vertex operators can be constructed in various ``pictures. Recently this was discussed in the context of pure spinor formalism. NSR picture changing operators have an elegant super-geometrical interpretation. In this paper we provide a generalization of this super-geometrical construction, which is also applicable to the pure spinor formalism.
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 massless four-point amplitude. It encodes bosonic and fermionic external states in supersymmetric form and reduces to existing bosonic amplitudes when expanded in components, therefore proving their equivalence. We also show how to compute the kinematic structures involving fermionic states.
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 $S^2$.
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