Live blogging: Huggett

On to part 2, Duality!

Strings can wrap around a compact dimension, which leads to a number w, the ‘winding number’ of the string.  Classically one would expect that to be fixed, but when we get interactions w will be able to change, i.e. be dynamic, and will have a corresponding quantum number.

Huggett goes on to explain T-duality.  Winding and momentum can change roles (n <–> w) in the Hamiltonian (and R <–> 1/R) .  The dynamics of the spatial wavefunction becomes the dynamics of the winding wavefunction in the dual, and vice-versa…  the pattern of observed quantities is preserved.  T-duality is like a translation manual between two theories.

This raises Huggett’s 3rd question: How should we understand T-duality?  Do duals describe physically distinct situations?

 

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One thought on “Live blogging: Huggett

  1. In brief, given the strategy described by Carl, both winding and momentum are represented by wavefunctions living in on circles – momentum in physical space, with radius R, and winding in a ‘new’ space of radius 1/R. If you now consider a dual system in which physical space has radius 1/R, it follows that the winding wavefunction lives in a space of radius 1/(1/R) = R. If you also exchange the momentum and winding wavefunctions, then nothing changes – except which space is physical space. But is that any change at all?

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