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B Branes, gluons, time reversal, and string theory.

  1. Oct 14, 2017 #1
    So a gluon in string theory may be an open string whose ends live on one or two branes?

    These strings have an orientation along the string?

    Does the orientation change direction if we reverse time, some where I thought I read that one can think of a flow along the string so if you reverse time the flow must reverse?

    Can we think of each end of the string as being associated with a color charge and an anti color charge, like red/antiblue?

    Thanks for any help!
  2. jcsd
  3. Oct 14, 2017 #2

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  4. Oct 19, 2017 #3
    In quantum field theory (and in string theory), the standard framework for thinking about these things, is in terms of C (charge), P (parity), and T (time) transformations. C swaps particles with their antiparticles, P is a reflection (swaps left and right), and T is time reversal. There is a famous theorem, the CPT theorem, which says that a quantum field theory is "invariant" under the combined CPT transformation (in which all three of these changes are applied simultaneously). So if your theory allows a particular physical process, it must also allow the CPT-transformed counterpart.

    Unfortunately this is a part of physics where my understanding is pretty shallow. If I worked through a few of the CPT proofs, and really thought about what was going on, I might have more to say. One of the complications is that defining C, P, and T is not always straightforward. You have to define algebraically how they act on all the observables of the theory under consideration - how all the various types of field (scalar, spinor, vector, tensor...) transform. In string theory there is the additional complication that CPT "inside the string" (on its worldsheet) is a different thing to CPT in the space-time that it moves through.

    So I can look up papers where they talk about CPT, but for me it's just opaque algebra - do all these transformations, and a certain thing happens. In particular, I haven't made that intuitive connection between the algebra, and my private visualizations of reflection and time reversal, etc - the price of not having properly worked through it. In turn that means I can't fluently talk about the similarities and differences between a naive concept of reflection or time reversal, and the technical concept that is given that name. Hopefully in time I'll get there. But meanwhile I decided to jump in anyway and respond to this post, because it was just sitting there unanswered...

    Regarding the orientation of a string, it is not defined by anything like a physical flow from one point to another. You can certainly have e.g. a wave traveling along or around a string in a particular direction, but the string's "orientedness" is not due to the presence of anything like that, it doesn't require it. It's more that, in a so-called orientable space, you are able to define a difference between left and right, or up and down. You can switch the labels around, but there's still an absolute difference between one direction and the other.

    In terms of C, P and T as they are technically defined, I would think that time reversal, T, would not reverse the spatial orientation of a string. Instead, reversing the orientation of a string would correspond to P, reflection, the "parity transformation" that swaps left and right. Meanwhile, it's the combined transformation, CPT, which will actually give you the physical mirror process to what you started with (the "anti-process" which is also a solution of your theory); so along with T and P, you need to apply C, and invert any charges that the string may be carrying (whether they are located on its ends, as in an open string theory, or smeared around it, as in the heterotic string).
  5. Oct 19, 2017 #4
    It seems we are told in the copied text I posted that oppositely orientated strings have opposite charges at their ends and we know that time reversal changes particle to antiparticle. Using my limited knowledge, if we put the two together it seems that time reversal must change orientation?

    Thank you for your help Mitchell!
  6. Oct 19, 2017 #5


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    It helps, but at the cost of doing peculiar -or at least, not intuitive- associations between orientation, Chan-Paton charge and, whatever it is, string charge.

    It could be helpful to have also some description of the same phenomena (Chan Paton charges in the extremes of the string) for unoriented strings, and how one quotients across.
  7. Oct 21, 2017 #6
    String charge, like brane charge, ultimately refers to interactions with closed strings. Gravity is not the only field that comes from closed strings.

    Roughly speaking, the oscillations of a closed superstring are defined by a left-moving vector and spinor, and a right-moving vector and spinor. "Left-moving vector + right-moving vector" excitations include graviton, dilaton, and a "B-field". This B-field is the string charge. "Left-moving spinor + right-moving spinor" excitations are also bosonic; p-form fields for various values of p. These p-forms are the brane charge. ("Vector + spinor" excitations give you fermions: gravitino and dilatino.)

    Ultimately this is much the same as the charge of a point particle. The electric field of an electron is understood in terms of virtual photons originating in the electron. All these B-fields and p-form fields similarly describe the density of virtual closed superstrings (in various excitations) accompanying an open string or a brane, respectively. There's a word-sketch of all this in section 2.1 here; and a little more detail in slides 47 and 48 here. The real details take up a chapter or two in any superstring textbook.

    (@Spinnor: In his textbook, Zwiebach does say there's a current along the string. So there's something about how all these fields connect, at the point where a string joins a brane, that I don't get yet. @arivero: I think orientifold projection eliminates the B-field and half the p-form fields. What that means for the Chan-Paton labels, I also don't get yet.)
  8. Oct 21, 2017 #7
    I got the feeling you could answer any question about strings, no hope for me! o0)
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