Disoriented with unoriented and oriented open strings

[arivero]

Mi imaginery of a oriented string is a line with two different (oposite) ChenPaton labels pasted in the extremes, say +...- while an unoriented one has the same label pasted in both extremes, say +...+ or -...-

In this imaginery a vacuum loop for oriented strings would create two strings +...- and -...+ and they can only do a cylinder. On the other hand, unoriented strings can have a vacuum loop where the initial +..+ and -..- strings can rejoing to do a moebius strip. I ask that only opposite label can be joined when two strings join into one, and that a string must split to opposite labels. It seems to be adjusted to reason, as in any other case we would allow for self-aniquilation via an open string tadpole.

I can recover the same imaginery if I draw a worldline in the border of the worldsurface, so that the signs + and - correspond to a label going forward or backward in time. So it seems pretty consistent.

Now, if I keep on this idea, it happens that two unoriented strings can join to form an unoriented one: +...+ and -...- can join in +...(+-)...- and then evolve as a single +...- oriented string.

Also, two oriented strings will always join to form a oriented string, and the join of an oriented plus an unoriented string will always form an unoriented one. And notice, an unoriented string will always break into an oriented string plus an unoriented one

So what is happening here? Does unoriented string theory include the oriented string? I was used to hear the contrary: that we get the unoriented theory as a quotient of the oriented one.

 

[arivero]

I am still disoriented... any guide here?

In fact I am now worse than six years ago as now I find myself compating with QCD, and thinking that an oriented string is one with mesons while an unoriented string has also diquarks and antidiquarks. So it seems that, when suplemented with charges, the unoriented string has more states.

And same paradox with closed: We call "extended Virasoro-Shapiro model" to the oriented bosonic theory, and "restricted Virasoro-Shapiro" to the unoriented one. And "restricted" has less states than "extended", has it?

 

[arivero]

Point today is, if I decide that I want to label a string theory, say a Veneziano model, with n quarks, then I get an U(n) gauge group, or SU(n) if there is some argument to kill the singlet away (is there some?).

But I could reverse an arrow of the three-pions vertex and then it transforms to a diquark-pion-(anti)diquark vertex. Does this reversal imply that now we are using an unoriented string? The gauge group seems to be O(2n) with the states in the symmetric representation. The intuition here is that SO(2n), or Sp(n) for the same tokem, decomposes down to SU(n) producing the adjoint plus the two conjugate copies of the symmetric, that should be the mesons, the diquarks and the antidiquarks. Another way to tell the same history is that the antiparticles of SU(n) have been promoted to "particles" in SO(2n), so that where we had a $N$ and $\bar N$ of SU(n) we now have a 2N of SO(2n) joining both.

But then, if this O(2n) or Sp(n) theory is an unoriented one, and it is the quotient of an oriented theory, it should be of U(2n)

So intuitively it seems we have a chain U(2n) oriented ---> O(2n) unoriented ---> U(n) oriented

But I have not seen such double chain described in the literature, so intuition is failing. The question is, is it failing a lot?

 

[mitchell porter]

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 fermionic 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. David Tong 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 this paper, 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 "D-Brane Primer", which is where I always start when I want to see how open strings come from D-branes.

 

[arivero]

The drawing of Armoni looks very as boundary condition marks in Mandelstam formalism for the light cone.

I think there is something I am missing. To recapitulate:

Type II are oriented strings and closed,
Type I are unoriented and open,
and Type I includes a portion of the closed IIB via orientifold quotient.

Now, where are the unoriented open? They could be type II via D-Branes, or type I via restriction to the [adjoint of] U(n) subgroup. Does the literature discuss both cases?