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Emergence of Superstring from Pure Spinor

  1. Jun 19, 2011 #1


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    Emergence of Superstring from Pure Spinor

    Ichiro Oda
    (Submitted on 17 Jun 2011)
    Starting with a classical action where a pure spinor $\lambda^\alpha$ is only a fundamental and dynamical variable, the pure spinor formalism for superparticle and superstring is derived by following the BRST formalism. In this formalism, not only the string variable $x^m$ but also the space-time spinor $\theta^\alpha$ are emerged as the Faddeev-Popov (FP) ghosts of a topological symmetry and its reducible symmetry. This study suggests that the fundamental theory behind the pure spinor formalism of the superstring might be a topological field theory.


    I thought that the title of this paper was totally ambitious, so, I am posting it here for comments. Mitchel Porter and others, what can you say about this paper? Is it really amazing as the title implies?
    Last edited: Jun 19, 2011
  2. jcsd
  3. Jun 19, 2011 #2
    The second paragraph has to be the most succinct explanation ever of what the pure spinor formalism is about, and the third paragraph is the ingenious idea behind the paper in one sentence. It certainly starts well...
  4. Jun 21, 2011 #3
    I believe I now understand the paper somewhat better.

    In perturbative string theory, you use a d=2 CFT which lives on Riemann surfaces (the worldsheet of interacting strings). Normally, the CFT includes some bosonic fields (the space-time coordinates of the string), some fermionic fields (superpartners of those coordinates), and ghost fields from BRST quantization. In the pure spinor formalism, the ghosts are http://en.wikipedia.org/wiki/Pure_spinor" [Broken].

    http://arxiv.org/abs/1105.1147" [Broken], Berkovits proposed to start with the bosonic fields and the pure spinor fields, and to derive the fermions as the ghosts. (Lisi wanted to do something similar with E8 theory, but the difficulty is to get the right statistics for the ghosts.) Usually you would use a "Virasoro constraint", but here he used a d=10 generalization of the constraint from twistor theory. The resulting theory is supersymmetric, so he calls it supersymmetry emerging from a twistor-like constraint.

    Oda wants to go further and have the CFT bosons emerging as ghosts as well. So he would be starting with a worldsheet CFT consisting of nothing but pure spinors, with the bosons emerging as "ghosts for ghosts", second-order ghosts for the fermionic ghosts.
    Last edited by a moderator: May 5, 2017
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