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Has anyone heard of Anyonic strings?

  1. Jan 28, 2009 #1

    MTd2

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    Anyon are particular 2 dimensionsional objects and so is the worldsheet critical superstrings. But given that those 2 are extemely fashionable nowadays, and they happen in this dimension, I am extremely surprised to find that anyone didn't try anyonic strings. That is, instead of supersymmetric, one would get an anyon relation.

    Anyway, I relly don't like supersymmetry because they are not generic enough, because they just relate fermions and bosons. Personal taste, really. Maybe relations between anyons and supersymmetry might have a relation. I don't know.

    Any hint?
     
  2. jcsd
  3. Jan 29, 2009 #2
    Well, remember first that anyons arise due to the non-trivial representations of the permutation (or better: braid) group in 2+1 dimensions. In that same train of thought it follows that there are no anyons in higher dimensions. At least not in the same literal sence.

    On the other hand, anyons are closely related to topological quantum field theories, Chern-Simons theory in particular. TQFT's in higher dimensions are indeed employed in string theory, although don't ask me in what way.
     
  4. Jan 29, 2009 #3

    MTd2

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    Sure, you are right. I had this mental image of anyons in a plane, because of the usual examples in condensed matter QM, where time is just a paramter. I totaly forgot that the time dimension was not being counted. So you are right, if there is any relation with a string theory, it should be a topological one.

    Yes, after your tip, I've found some interesting things:

    Exotic Strings statitics, a post by Urs Schreiber:
    http://golem.ph.utexas.edu/string/archives/000777.html


    Fractional quantum Hall effect and nonabelian statistics
    http://arxiv.org/abs/hep-th/9202001
    and the articles that cites it:
    http://arxiv.org/cits/hep-th/9202001

    Exotic Statistics for Strings in 4d BF Theory:
    http://arxiv.org/abs/gr-qc/0603085

    Links, Quantum Groups, and TQFT's
    http://arxiv.org/abs/q-alg/9506002v2

    Quantum field theories of vortices and anyons
    http://www.projecteuclid.org/DPubS?...e=UI&handle=euclid.cmp/1104178064&page=record

    Interesting stuff that I found while I was searching:


    Topological Quantum Computation:
    http://www.theory.caltech.edu/~preskill/talks/Preskill_Biedenharn4.pdf

    An Anyon primer:
    http://arxiv.org/abs/hep-th/9209066

    Exact Solutions in Einstein-Chern-Simons Electrodynamics
    http://icpr.snu.ac.kr/resource/wop.pdf/J01/1992/025/R03/J011992025R030274.pdf
     
    Last edited: Jan 29, 2009
  5. Jan 30, 2009 #4
    Funny that you mention those. I'm actually starting my PhD on topological systems and its relation to topological quantum computation, with emphasis on the fractional quantum Hall effect. I recommend this review article in particular:

    Non-Abelian Anyons and Topological Quantum Computation
    http://arxiv.org/abs/0707.1889
     
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