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Physics
Beyond the Standard Models
Disoriented with unoriented and oriented open strings
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[QUOTE="mitchell porter, post: 5802255, member: 103130"] In the modern understanding of open strings, D-branes come first. Open strings are fluctuations of D-branes. If there are no branes in the picture, you only have closed strings. Even the open strings of Type I turn out to be attached to space-filling D9-branes. A Chan-Paton factor comes from such branes. I thin one can also say that whether or not a string is oriented, depends on whether its worldsheet, considered as a manifold (i.e. Riemann surface), is orientable. If it is an orientable manifold, like a 2-sphere, or a 2-torus with n holes, then by default it corresponds to an oriented string. For such a manifold to describe the worldsheet of an unoriented string, you have to identify reflections. But now non-orientable manifolds like Mobius strip and Klein bottle also correspond to possible string histories, and form part of the path integral. Sphere, torus, Klein bottle... are topologies of closed string histories. Histories with open strings will correspond to 2-manifolds with boundaries, like the Mobius strip. The question as to whether a fundamental diquark string is possible or not, is a question about the possible labels or quantum numbers that can circulate on those boundaries. I don't feel in a position to give a definitive answer. (In fact, ideally everything I say here should be checked against an authoritative source, like a textbook or review paper. This is just an informal synopsis of what I have picked up from the literature so far.) But it's clear that in the modern understanding, it's the properties and possibilities for the D-branes that determine the possible edge labels. In general, I would have assumed that a diquark string is not a well-defined object, just because a diquark is not a gauge-invariant object in field theory. However, I do see one theorist talking about diquark strings - Adi Armoni. Interestingly, he seems to talk only about [I]fermionic[/I] strings with a quark at either end. What does that refer to? In terms of field theory, it seems to mean two quarks, connected by a flux tube, with a third fermion that is delocalized along the tube. Furthermore, this third fermion has to be in the antisymmetric representation. So it might sound like a rather specialized concept, with no particular relationship to fundamental strings. [URL='http://www.damtp.cam.ac.uk/user/tong/talks/dbrane.pdf']David Tong[/URL] has talked about the situations in which domain walls and flux tubes in field theory do map directly onto branes and strings in a string theory, and there aren't many examples. However, Armoni says that his unoriented diquark string really does map onto a fundamental string - an unoriented string from a class of orientifold models introduced by Sagnotti in the 1990s. See [URL='http://arxiv.org/abs/0901.4508']this paper[/URL], page 7 for a picture of an unoriented fermionic diquark string, page 8 for the reference to Sagnotti. That's a long way to go, and a lot of work, to find just one example of a fundamental diquark string. I have not done the work to understand what Sagnotti did. However, there is a section on orientifolds (part 3.9) in Clifford Johnson's [URL='http://arxiv.org/abs/hep-th/0007170']"D-Brane Primer"[/URL], which is where I always start when I want to see how open strings come from D-branes. [/QUOTE]
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Beyond the Standard Models
Disoriented with unoriented and oriented open strings
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