Perhaps due to a gap in my learning I don't know why I don't see bosonic excitations $\alpha_n^{i}$ discussed in superstring theory, only fermionic excitations $\psi_r^i$. I know the NS sector contains bosons and the R sector fermions. In my reading of Polchinski vol. 2, I don't see any mention of states like

$$\alpha_n^{i} |0\rangle_{\text{NS}}.$$

Is this because these states are massive, so of less concern? Do they exist in the superstring? Can they be applied to the spinor $|0\rangle_{\text{R}}$?

  • $\begingroup$ he doesn’t discuss them in volume 2 because he already did in vol 1. and yes they also play a major role in the superstring, and they can be applied to Fock ground states $\endgroup$ – Wakabaloola Aug 8 at 8:09
  • $\begingroup$ I think the correct answer to my question is: it suffices to discuss only fermionic excitations, as these are related by supersymmetry to bosonic excitations. For instance, if we considered $e_{ij} \alpha_{-1}^i \tilde \alpha_{-1}^j |0\rangle_{NS}$ AND $e_{ij} \psi_{-1}^i \tilde \psi_{-1}^j |0\rangle_{NS}$ we'd be double counting the dilaton, graviton, and antisymmetric rank-2. $\endgroup$ – Dwagg Oct 20 at 14:35
  • $\begingroup$ If I'm wrong please do correct me. $\endgroup$ – Dwagg Oct 20 at 14:36

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