Abstract
The sectorized description of the (chiral) heterotic string using pure spinors has been misleadingly viewed as an infinite tension string. One evidence for this fact comes from the tree level 3-point graviton amplitude, which we show to contain the usual Einstein term plus a higher curvature contribution. After reintroducing a dimensionful parameter ℓ in the theory, we demonstrate that the heterotic model is in fact two-fold, depending on the choice of the supersymmetric sector, and that the spectrum also contains one massive (open string like) multiplet. By taking the limit ℓ → ∞, we finally show that the ambitwistor string is recovered, reproducing the unexpected heterotic state in Mason and Skinner’s RNS description.
Highlights
This issue did not receive much attention until one of the authors, inspired by the works of Chandıa and Vallilo [5, 6], developed a new pure-spinor model, referred to as the sectorized heterotic string in the present paper, in which the BRST charge is modified with respect to the original proposal by Berkovits and the description of supergravity states was made possible [7]
The sectorized description of the heterotic string using pure spinors has been misleadingly viewed as an infinite tension string
As a consistency check for the new BRST charge, the sectorized string was later coupled to a generic heterotic background [8] and we were able to show that requiring nilpotency of the BRST charge is equivalent to imposing the classical constraints on the background superfields, which had been previously shown by Berkovits and Howe to imply the supergravity and super Yang-Mills equations of motion [9]
Summary
The action for the heterotic sectorized string in the pure spinor formalism is given by. The N = 1 supersymmetry of the heterotic string is compatible with the sectorized formulation and all the operators displayed in (2.3) are invariant under the supersymmetry charge qα =. We were able to show in [8] that the model imposes the correct (on-shell) constraints when coupled to a generic heterotic background As another test for the sectorized model, we can compute the 3-point, tree-level correlation function of gravitons using the vertex operator (2.9a), as we show in the following subsection. String, one would expect the 3-point graviton amplitude to give rise to the usual expression coming from Einstein gravity. The 3-point scattering amplitude at tree level is given by the usual correlator of three vertex operators inserted at arbitrary points zj on the 2-sphere: U(1)(z1)U(2)(z2)U(3)(z3).
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