Abstract
Constructing a consistent four-dimensional Lagrangian for charged massive higher-spin fields propagating in an electromagnetic background is an open problem. In 1989, Argyres and Nappi used bosonic open string field theory to construct a Lagrangian for charged massive spin-2 fields in a constant electromagnetic background. In this paper, we use the four-dimensional hybrid formalism for open superstring field theory to construct a supersymmetric Lagrangian for charged massive spin-2 and spin-3/2 fields in a constant electromagnetic background. The hybrid formalism has the advantage over the RNS formalism of manifest mathcal{N} = 1 d=4 spacetime supersymmetry so that the spin-2 and spin-3/2 fields are combined into a single superfield and there is no need for picture-changing or spin fields.
Highlights
Electromagnetic background in four dimensions and writing down the effective Lagrangian for the above-mentioned resonances are still unsolved
The hybrid formalism has the advantage over the RNS formalism of manifest N = 1 d=4 spacetime supersymmetry so that the spin-2 and spin-3/2 fields are combined into a single superfield and there is no need for picture-changing or spin fields
Open bosonic string field theory was used by Argyres and Nappi to construct a consistent theory of charged massive spin-2
Summary
We introduce the manifestly four-dimensional spacetime supersymmetric description of the superstring. The worldsheet action, relevant variables and their main properties are presented, as well as a formulation in terms of oscillator modes for the case without a background U(1) gauge field. We refer to the original works [20,21,22], by one of the authors, and [23]. Our conventions for the worldsheet theory follow [24] and we are using α. For manipulations with sigma matrices and dotted/undotted spinor indices we utilize the conventions in the appendix of [25], for example, xαα = σαmαxm, σmαασβmβ = −2δβαδβα ̇ , (ψχ) = ψαχα, (ψχ) = ψαχ ̄α , (σmσn + σnσm)αβ = −2ηmnδαβ, etc
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