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Register a new userOn worldsheet curvature coupling in pure spinor sigma-model
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We discuss the relation between unintegrated and integrated vertex operators in string worldsheet theory, in the context of BV formalism. In particular, we clarify the origin of the Fradkin-Tseytlin term. We first consider the case of bosonic string, and then concentrate on the case of pure spinor superstring in $AdS_5times S^5$. In particular, we compute the action of $b_0 - bar{b}_0$ on the beta-deformation vertex. As a by-product, we formulate some new conjectures on general finite-dimensional vertices.
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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 an action for the pure spinor sigma-model in $AdS_5times S^5$. From the point of view of the BV formalism, this sigma-model belongs to the class of theories where the expansion of the Master Action in antifields terminates at the quadratic order. We show that it can be reduced to a simpler degenerate sigma-model, preserving the AdS symmetries. We construct the action of the algebra of worldsheet vector fields on the BV phase space of this minimalistic sigma-model, and explain how to lift it to the original model.
We derive the Free Differential Algebra for type IIA supergravity in 10 dimensions in the string frame. We provide all fermionic terms for all curvatures. We derive the Green-Schwarz sigma model for type IIA superstring based on the FDA construction and we check its invariance under kappa-symmetry. Finally, we derive the pure spinor sigma model and we check the BRST invariance. The present derivation has the advantage that the resulting sigma model is constructed in terms of the superfields appearing in the FDA and therefore one can directly relate a supergravity background with the corresponding sigma model. The complete explicit form of the BRST transformations is given and some new pure spinor constraints are obtained. Finally, the explicit form of the action is given.
We propose boundary conditions on a two dimensional 6-vertex model, which is defined on the lightcone lattice for an open string worldsheet. We show that, in the continuum limit, the degrees of freedom of this 6-vertex model describe a target space coordinate compactified on a circle of radius R, which is related to the vertex weights. This conclusion had already been established for the case of a 6-vertex model on the worldsheet lattice for the propagator of a closed string. This exercise illustrates how the Bethe ansatz works in the presence of boundaries, at least of this particular type.
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
to calculate the kinematic factors of the one-loop and two-loop massless four-point amplitudes involving two and four Ramond states.
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