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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 26th 2010

    expanded brane

    first a little remark on what D-branes are abstractly, in reply to an MO-question, then something on fundamental branes, going along with the discussion on the Café

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeDec 7th 2015

    I have expanded and polished the Idea-section at brane a little more.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 30th 2019

    added pointer to

    diff, v53, current

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeNov 28th 2019

    In a casual search to find out what it is for branes to coincide, I came across these slides

    • Callum Brodie, Coincident M5-branes and dual singular geometries, slides

    There they are at slide 3 (7 of 54).

    It’s odd. You start out from a schoolchild impression thinking of the subatomic world as a collection of identifiable, point-like particles, then give all this up with whatever quantum understanding you can muster to some sense of particles as excitations of quantum fields. When you peek ahead to see what’s happening at the frontier, they’re drawing pictures of classical-looking higher-dimensional objects sitting calmly next to each other!

    • CommentRowNumber5.
    • CommentAuthorLuigi
    • CommentTimeMay 6th 2020

    Added link to exotic branes

    diff, v55, current

    • CommentRowNumber6.
    • CommentAuthorLuigi
    • CommentTimeMay 6th 2020

    Added link to exotic branes

    diff, v56, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeMay 6th 2020

    Belated reply to #4:

    There is a plethora of subtly different aspects to the concept of “brane”, which is usually well-hidden beneath the colloquial use of the word in the literature.

    One key distinction is that between “black branes” and “fundamental branes”:

    A “black brane” is a solution to a classical field equation of a higher dimensional supergravity theory. Of particular interest are the BPS solutions among these, which are those black branes that carry the maximally possible electromagentic charge (or rather the appropriate higher gauge field analog). This turns out to be such that the electromagnetic repulsion of such extremal/BPS black branes exactly cancels against their gravitational attraction. As a result, configurations of a bunch of such branes happily sitting next to each other is again a solution to the corresponding equations of motion (provably).

    Next, there is a correspondence, mainly by inspection of transformation properties and charges (“quantum numbers”) between the types fundamental branes (Green-Schwarz sigma models) and those of black branes. This relates concepts in different regimes of understanding: Fundamental branes are perturbative, weakly coupled quantum objects (not back-reacting onto their target spacetime geometry), while black branes are non-perturbative strongly coupled classical objects. If/when both are BPS, then non-renormalization arguments due to “supersymmetry protection” indicate that their core properties (charges) should be independent of the choice of coupling constant. Therefore, one imagines that in the putative non-perturbative formulation of the theory (M-theory) it should be possible to see that fundamental branes and black branes are the same kind of object, seen in different regimes.

    That’s one reason why people are at easy drawing these classical configurations of branes that are so very non-quantum. It’s a good reason – if one remembers that and where a fair amount of speculation/handwaving/educated guesswork is involved.

    But the main reason people speak this way is a certain kind of conceptual carelessness. Faced with an wildly complex theory, they throw all caution in the wind and proceed following naive intuition, trained on having deeply immersed themselves in the subject, or in what’s known about the subject.

    Again, this is not necessarily bad, but clearly it can go wrong if one forgets that and where strong unproven assumptions have been made. A grand example is the current debate about consistency of KKLT-type string vacua: This is all about knowing what it acutally means to “add some D3-branes” or to “add some O-planes” to a supergravity solution. 15 years ago, KKLT felt they have good enough intuition about this to make a strong claim, and thousands of articles followed suit. 15 years later, serious doubts arose. Now they have conferences where they have show-of-hands on who believes what. (This is not a joke. )

    • CommentRowNumber8.
    • CommentAuthorDavid_Corfield
    • CommentTimeMay 6th 2020

    Thanks, that’s helpful!