Has anyone heard of Anyonic strings?

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In summary, anyons are particular 2 dimensional 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.
  • #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?
 
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  • #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.
 
  • #3
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
 
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  • #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
 

Related to Has anyone heard of Anyonic strings?

1. What are Anyonic strings?

Anyonic strings are theoretical one-dimensional objects in quantum field theory that are thought to exist in certain systems. They are described as strings because they have properties similar to those of physical strings, such as tension and length, but they are made up of particles known as anyons instead of atoms or molecules.

2. How are Anyonic strings different from regular strings?

Anyonic strings have unique properties that distinguish them from traditional strings. They are formed from anyons, which are particles with fractional spin and exotic quantum statistics. This allows them to interact with each other in ways that cannot be explained by classical physics.

3. What are some potential applications of Anyonic strings?

Anyonic strings are still a theoretical concept and have not yet been fully observed or studied. However, they have generated interest in the scientific community due to their potential applications in quantum computing and topological quantum phenomena. They may also have implications in the study of black holes and string theory.

4. Has anyone observed Anyonic strings?

Currently, there is no direct observation of Anyonic strings. However, there have been experiments that have indirectly observed the behavior of anyons, which supports the existence of Anyonic strings. Further research and advancements in technology may eventually allow for the direct observation of Anyonic strings.

5. How do Anyonic strings relate to the study of topological phases of matter?

Anyonic strings are closely related to topological phases of matter, which are states of matter that cannot be described by conventional symmetry breaking. Anyonic strings are believed to play a crucial role in the formation of these phases in certain systems, and their study can provide insight into the behavior of matter at a fundamental level.

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