Twistor Origin of the Superstring

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Discussion Overview

The discussion revolves around the concept of the twistor origin of superstring theory, particularly focusing on the implications of introducing a pure spinor in ten-dimensional space-time. Participants explore the relationship between twistors, spinors, and the quantization of superstring theory, as well as comparisons to other theories.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants discuss the twistor constraint as a 16-dimensional space formed by pairs of 8-dimensional spinors, suggesting a connection to gauge symmetry in bosonic strings.
  • Others express uncertainty about the implications of the twistor constraint and its relation to the gauge symmetry, indicating a need for clarification.
  • A participant notes that the paper introduces a ten-dimensional bosonic spinor and discusses the role of ghost fields as worldsheet fermions in the superstring framework.
  • One participant mentions a comparison to Garrett Lisi's E8 theory, highlighting skepticism about deriving standard model fermions from ghost fields.
  • A participant attending a talk by Nathan Berkovits expresses uncertainty about their expertise to contribute meaningfully to the discussion.
  • Another participant points out that Berkovits has not yet demonstrated how physical fermion states can be derived from the ghost fields mentioned in the paper.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and skepticism regarding the implications of the twistor approach to superstring theory. There is no consensus on the clarity or validity of the claims made in the paper, and multiple viewpoints remain unresolved.

Contextual Notes

Some participants indicate a lack of familiarity with the topic, which may limit their ability to engage with the technical details. There are also references to other theories and ideas that may not be fully explored within this discussion.

Who May Find This Useful

This discussion may be of interest to those studying advanced topics in string theory, twistor theory, or the relationship between gauge symmetries and fermionic states in theoretical physics.

mitchell porter
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http://arxiv.org/abs/1409.2510
Twistor Origin of the Superstring
Nathan Berkovits (ICTP-SAIFR/IFT-UNESP, Sao Paulo)
(Submitted on 8 Sep 2014)
After introducing a d=10 pure spinor λα, the Virasoro constraint ∂xm∂xm=0 can be replaced by the twistor-like constraint ∂xm(γmλ)α=0. Quantizing this twistor-like constraint leads to the pure spinor formalism for the superstring where the fermionic superspace variables θα and their conjugate momenta come from the ghosts and antighosts of the twistor-like constraint.

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We should compare this with Ichiro Oda's "Emergence of Superstring from Pure Spinor".
 
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Let me see if I understand something of the idea. The twistor constrain is a 16 dimensional space, which are spanned pairs of 8 dimension spinors, related by supersymmetry. So, what you have here is bosonic string, where each pair of spinors is a de-bosonized field. And this constrains yield the gauge symmetry of the string.
 
Note. I am trying to understand! Do not take what I posted above seriously! I am waiting for an answer too if that makes sense!
 
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What I understood so far (I had very little time to read it) was that he starts with ten space-time dimensions and a ten-dimensional bosonic spinor. Then he makes a quantum theory for strings in this space, and there are ghost fields which are the worldsheet fermions of the superstring.

I remember that Garrett Lisi (E8 theory) was mocked for hoping that he could get standard model fermions from ghosts somehow...
 
Actually I'm sitting in a talk right now by Nathan on this very paper, but I'm not sure I'm expert enough to offer an opinion. :P
 
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He appears to be saying he hasn't yet shown explicitly how physical fermion states can be obtained from the ghosts.