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A Problems with quantizing branes in string theory

  1. Dec 24, 2016 #1


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    Dear all,

    recently I'm reading up some string/M-theory, especially the role of branes, because I'm writing a popular science book in Dutch. Every textbook states the issues one encounters when you try to quantize p-branes for p>1, as is discussed e.g. here:



    1) non-renormalizability
    2) continuous particle spectrum
    3) existence of spikes which result in non-locality

    So, the moral then is: strings are magic, strings it will be. But later in the story branes re-enter the game, via D-branes and e.g. 2- and 5-branes in D=11 sugra and M-theory. So my questions are:

    *) What happens to the objections we had which made us to prefer strings above p>1-branes and reject them? Why can we suddenly consider branes to be consistent after all? Does it have to do with their solitonic character instead of being fundamental objects like strings?
    *) Do we have a Polyakov-like formulation for branes as for strings, by introducing auxiliary fields?
    *) Where can I find a pedagogical treatment on the quantization of branes and the issues I mention here? The standard textbooks like Becker2Schwarz, Johnson etc. don't seem to answer my questions.

    Merry X-mas and all the best!
  2. jcsd
  3. Dec 26, 2016 #2


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    I do not know very much about the topic and I hope that someone will have answers because I have exactly the same questions.
    For the first question, I think that the point is that the arguments against p-branes were all based on perturbation theory. But they are essentially non perturbative entities and then all the objections fall on the side. But someone else may correct me about this.

    Merry X mas too!
  4. Dec 27, 2016 #3
    If I was going to study the quantization of membranes, I'd look at works by Paul Dirac, Michael Duff, Washington Taylor, and David Berman. Dirac did the original study of the quantum membrane, Duff of the quantum supermembrane. Taylor wrote some reviews of matrix models of quantum branes around 2000-2001, and during the last decade, Berman has written a number of review papers on M-branes in the era of AdS/CFT.
  5. Dec 27, 2016 #4


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    Thanks for the references! I'm now reading some papers in a collection of papers called "The world in eleven dimensions",


    . I'm getting the impression that the usual "we can only quantize p<2 branes without technical problems" is circumvented by the idea that branes are non-perturbative objects, as mentioned by nrqed. What puzzles me is that I can't seem to find a single paper or textbook in which this is explicitly stated, whereas every textbook on string theory warns for all the doom and evil one encounters if you try to quantize beyond strings. Strange.
  6. Dec 29, 2016 #5


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