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We have many fields in higher dimensional string theory for charges (B field, C field, RK, RR). Are these fields made up of individual particles like how the EM field is made up of photons? Or do they just have no exchange particles and just carry a strength when produces by strings/ branes?

Urb
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3 Answers3

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Those fields, fluxes, etc come from particular closed string modes. (The graviton is just one mode of the closed string.) For example see slides 48, 49 here.

Mitchell Porter
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  • Minor comment to the post (v1): Please consider to mention explicitly author, title, etc. of link, so it is possible to reconstruct link in case of link rot. – Qmechanic Mar 14 '21 at 11:35
  • @Mitchell Porter. Just a comment, closed string modes does not produce RR-fields because perturbative string states cannot be charged under them (equivalently, there are no vertex operators for RR p-form fields). – Ramiro Hum-Sah Mar 15 '21 at 01:57
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    @Ramiro Hum-Sah Thanks for your comment. I guess I assumed that RR fields come from the RR sector of the string. Am I missing something? – Mitchell Porter Mar 15 '21 at 05:54
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This is a comment. I hope you get an answer by an expert in strings.

Roughly: string theory is an extension of quantum mechanics and should be consistent with quantum field theory. In QFT the fields are inactive, the photon field etc. over all space time. They are not composed by individual particles, they are a system where creation and annihilation operators generate and annihilate the named particles. I expect that this will be true in a more convoluted way with the fields defined in string theory.

anna v
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The Ramond-Ramond field is a higher gauge field and they are sourced by D-branes which are charged under them. In this sense, they are just like the electromagnetic field which is an ordinary gauge field. To get exchange particles, that is quanta, one would quantise the superstring in a background supporting such a field.

Mozibur Ullah
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  • I'm not sure that the statement "To get exchange particles, that is quanta, one would quantise the superstring in a background supporting such a field." is true. Fundamental strings are not charged under RR-form fields; then, even if you achieve a successful quantization (which is certainly impossible in the RNS formalism) I cannot understand how do you plan to obtain the particles whose "exchange" mediates a "RR-flux" interaction. – Ramiro Hum-Sah Mar 15 '21 at 00:09
  • @Ramiro Hum-Sah: the point I was making in the first sentence, is that I was emphasing that a RR field being sourced by a D-brane was akin to a classical field. The missing word in the second sentence is "expect", in that I expected that quantising the superstring, we would find quanta for such fields. – Mozibur Ullah Mar 17 '21 at 12:43
  • @Ramiro Hum-Sah: Are you saying that it is impossible to quantise the superstring? – Mozibur Ullah Mar 17 '21 at 12:48
  • @Ramiro Hum-Sah: If I was expecting the analogy to hold, then I should have said that I expect that quantising D-branes should give us quanta for RR fields. – Mozibur Ullah Mar 17 '21 at 12:53
  • Of course I'm definitely not saying that it is impossible to quantize the superstrings. I'm just saying that we should be very careful when drawing analogies between gauge and RR fields. RR-fields cannot be described as "exchange of quanta" because no asymptotic string states are charged under them, then there is no possibility of describe RR-fields by means of Feynman diagrams in string theory (that's what this question was asking for). RR-field can be discovered by quantizing the string but that does not imply that they can be treated in the same way as gauge fields. – Ramiro Hum-Sah Mar 17 '21 at 14:47
  • My comment about the quantization of the superstring was in the context of RR-backgrounds by using the RNS-formalism. I'm not aware of a single example of a successful quantization of the superstring in this context. – Ramiro Hum-Sah Mar 17 '21 at 14:58
  • @RamiroHum-Sah are you talking about the non-polynomial action when you have RR-backgrounds in the RNS formalism? Can you make it work in the pure spinor formalism? – Nihar Karve Mar 18 '21 at 07:28
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    @NiharKarve Yeah, I'm part I'm talking about this. But let's be clear, my point is simply that there are no perturbative string states charged under RR-fields, therefore is not correct to say that RR-fields are are analogous to gauge fields in the sense that both can be described by Feynman diagrams because RR-fields can't be treated in that way, in the general case. This is what the question was asking for. – Ramiro Hum-Sah Mar 18 '21 at 15:48
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    @NiharKarve Concerning strings on RR-backgrounds. I'm just saying that strings in RR-backgrounds are difficult to quantize in the RSN formalism, maybe that could be circumvented with the pure spinor formalism, sure; but my point is that this is not obvious and, again, I 'm not aware of anyone that can treat a RR-field states using a perturbative scheme (even a non-polynomial one) in analogy with gauge fields, that's what the author of the question was trying to know. – Ramiro Hum-Sah Mar 18 '21 at 15:48
  • @Ramiro Hum-Sah: I didn't say that as gauge fields they could be described through Feynman diagrams - that's your extrapolation. To me, gauge fields are classical. – Mozibur Ullah Mar 19 '21 at 21:18
  • @MoziburUllah The question was about whether or not, RR-fields can be described by an exchange of particles as in ordinary gauge theory; this is obviously a question about an analogy with the quantum mechanics of gauge fields, "exchange of particles" is translated into rigorous physics as "Feynman diagrams". The second phrase of your answer suggests that this is possible, but it is not. – Ramiro Hum-Sah Mar 20 '21 at 01:06
  • @MoziburUllah IIf for you gauge fields are classical, then I cannot understand why you answer in terms of classical gauge fields a question which is obviously about the quantum mechanics of gauge and RR-fields. – Ramiro Hum-Sah Mar 20 '21 at 01:10
  • @Ramiro Hum-Sah: The classical electromagnetic field is a gauge field, after quantisation it's no longer a gauge field although it's referred to as one. This is how I'm using terms. – Mozibur Ullah Mar 20 '21 at 08:30
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    @MoziburUllah Well, that idea is demonstrably wrong. After quantization gauge fields are still gauge fields. Gauge invariance should be preserved by the process of quantization, that's a basic phenomenological requirement. – Ramiro Hum-Sah Mar 20 '21 at 14:55
  • @Ramiro Hum-Sah: Good point, I suppose then we'd have to call them quantum gauge fields to distinguish them from classical gauge fields. – Mozibur Ullah Mar 21 '21 at 08:52