M Theory Lesson 3

In Lesson 2 we looked at a theorem relating surface moduli to Ribbon Graph moduli. This takes the form of an equivalence between categories. The ribbon graphs are indeed supposed to remind one of ‘t Hooft’s old diagrams for QCD, which appear in early String theory papers from the 1970s. But in Category Land one doesn’t play with Feynman diagrams based on a Minkowski background. No, no. The lesson of Penrose’s twistor theory is that sheaf cohomology is a good language for thinking about solutions to field equations. In Category Land and Machian physics this lesson takes on a whole new meaning, and one loses the desire to operate with Feynman diagrams at all. In twistor String theory one uses instead MHV diagrams, and things like gluon amplitudes become magically easier to compute. This is why a whole army of excited String theorists is currently busy calculating stuff for the LHC, quite convinced that they are doing QCD.

5 Responses so far »

  1. 1

    Mahndisa S. Rigmaiden said,

    11 20 06

    MHV diagrams look quite interesting! Thanks for the lesson.

  2. 2

    Carl said,

    Okay, NOW you’ve got my attention. MHV = “Maximal helicity violating”. The central interaction I deal with is \bar{\psi}_L\psi_R , which is a maximal helicity violation in its simplest form (and also is a mass term).

    AND, it’s not Lorentz covariant!

    One of the principles I believe the world is organized around is that when there is a simpler way of calculating something, that simpler way is closer to nature.

    I’m linking in the article by Cachazo, Svrcek and Witten.

  3. 3

    Kea said,

    Hi Carl

    Oh, yes. Simple is more right. No question about that. Eventually I will move onto the connection between MHV diagrams and Batanin’s magical mathematics.

  4. 4

    Kea said,

    You might also like the slides of Zvi Bern. He has a great one with thousands and thousands of Feynman terms, and then the 6 term MHV equivalent.

  5. 5

    L. Riofrio said,

    Having read through some of Penrose’s Road to Reality, there seems to be great hope for twistors and M-theory. Thanks for all the lessons.

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