Non-commutative geometry in ST?

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SUMMARY

The discussion centers on the relationship between non-commutative geometry (NCG) and string theory (ST), particularly in the context of D-branes. Participants highlight that the spacetime coordinates of coincident D-branes are represented as non-commuting matrices, suggesting a significant role for NCG in ST. A reference to Edward Witten's work indicates that NCG's application may differ from its connection to D-branes, particularly regarding the antisymmetric B-field in the massless bosonic sector. Additionally, a recommendation for the book "D-branes" by Victor Johnson is made for further exploration of these concepts.

PREREQUISITES
  • Understanding of D-branes in string theory
  • Familiarity with non-commutative geometry (NCG)
  • Knowledge of matrix representations in physics
  • Basic concepts of the antisymmetric B-field in string theory
NEXT STEPS
  • Study the implications of non-commutative geometry in string theory
  • Read "D-branes" by Victor Johnson for accessible insights
  • Explore Edward Witten's papers on non-commutative geometry and string theory
  • Investigate the role of the antisymmetric B-field in the massless bosonic sector
USEFUL FOR

The discussion is beneficial for theoretical physicists, string theorists, and researchers interested in the intersection of non-commutative geometry and string theory, particularly those focusing on D-branes and related concepts.

eigenguy
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I know that the spacetime position coordinates of D-branes become non-commuting matrices for coincident D-branes, but I'm not sure how or if this is related to the employment of NCG in ST.
 
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anyway, if noncommutative matrices can describe the coordinates of D branes, i am sure it would make sense that NGC plays a significant role in string theory. matrices --> geometry connection?
 
Originally posted by JasonJo
stop...

anyway, if noncommutative matrices can describe the coordinates of D branes, i am sure it would make sense that NGC plays a significant role in string theory. matrices --> geometry connection?

That's what I think too. But I was trying to decipher a paper by edward witten and near as I could tell, this use of NCG was distinctly different from the D-brane thing and had something to do with the antisymmetric B-field in the massless bosonic sector. Anyway, I just ordered a copy of "D-branes" by victor johnson and it apparently includes a more accessable discussion of it. I guess I'll see.
 

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