Abstract
We attempt to construct the full equations of motion for the Neveu–Schwarz and the Ramond sectors of the heterotic string field theory. Although they are also non-polynomial in the Ramond string field |$\Psi $|, we can construct them order by order in |$\Psi $|. Their explicit forms with the gauge transformations are given up to the next-to-next-to-leading order in |$\Psi $|. We also determine a subset of the terms to all orders. By introducing an auxiliary Ramond string field |$\Xi $|, we construct a covariant action supplemented with a constraint, which should be imposed on the equations of motion. We propose the Feynman rules and show how they reproduce well-known physical four-point amplitudes with external fermions.
Highlights
The Neveu–Schwarz (NS) sector of the heterotic string field theory was first constructed order by order in the coupling constant using the large Hilbert space of the superghosts [1]. It was completed by giving the action and gauge transformations in a closed form as a Wess–Zumino–Witten (WZW)-like theory [2], which is a natural extension of the similar formulation of the open superstring field theory [3]
The corresponding string products satisfy a set of identities with an additional derivation η characterizing the algebraic structure of the heterotic string field theory
We propose the Feynman rules to compute tree-level amplitudes in the heterotic string field theory by extending those for the open superstring [11]
Summary
The Neveu–Schwarz (NS) sector of the heterotic string field theory was first constructed order by order in the coupling constant using the large Hilbert space of the superghosts [1]. We will find a subset of terms in the equations of motion and the gauge transformations built with one or two string products to all orders. The explicit forms of the equations of motion and the gauge transformations will be given up to the next-to-next-to-leading order in .
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