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MTd2
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With one, we have 5, what about more than one? What are they? What are the importance of these, phenomenologicaly saying?
MTd2 said:With one, we have 5, what about more than one? What are they? What are the importance of these, phenomenologicaly saying?
MTd2 said:This is not ambiguous, I just didn't put it well, sorry. I mean string theory by a sigma model whose worldsheet has no conformal anomaly.With 1 supersymmetry, there are 5 theories, all of them shows that 10 dimension is a condition needed to cencel the anomaly. What if that sigma model, instead of 1 supersymmetry, had 2 or more? How many anomaly-free free would one get for each case? How many dimensions each one of them would have?
suprised said:What you are asking for are theories with more world sheet supersymmetries, yes they do exist, most famous is the so-called N=2 string for which the supersymmetries as written above are doubled. Its critical dimension is four, but this does not refer to Minkowski spacetime with signature (time,space)=(-,+++) but to a spacetime with signature (--,++); you may call that a two-time theory if you like...
suprised said:Be aware that these considerations are based on the world-sheet, which is not a fundamental concept but rather, by its very definition, a concept of perturbation theory. Thus non-perturbative relationships between those various strings are not visible in this framework; and the 11-dimensional membrane theory and the 12-dim F-theory are not describable in this language at all. So questions concerning the nature of string theory should not be formulated in this language in the first place.
MTd2 said:Sounds like what I see sometimes when I see Berkovitz talking about twistor strings. I see everywhere N=2 and (--++) signature. Anyway, couldn't one rotate (2,0) to (1,1)?
MTd2 said:But you have to to start counting dimensions somewhere, right? So the 10d strings spacetime is fundamental in this aspect. Also, isn't F-Theory a mathematical device to understand Type II strings?
suprised said:Well formally one can rotate the backround metric in the effective theory but then the theory is, I guess, not consistent any more. The theory in (--,++) is very special, has very few degrees of freedom, is integrable, etc, and probably not many of these special properties would survive this "wick" rotation. There is no reason why they should.
MTd2 said:But is that Berkovitz Twistor Theory? Also, when I said rotate, I didn't refer to rotate the metric, but rotate the chiralities, if that makes any sense. For example, like Left would be the x-axis and Right the y-axis. So, (2,0) or (1,1) would be a kind of coordinate.
MTd2 said:"All what matters that the Virasoro central charge is cancelled, and this requires a certain amount and structure of extra internal degrees of freedom."
That means string theory is a theory in without ghosts in surfaces?
suprised said:Rotating chiralities doesn't make sense IMHO.
Not always, how?suprised said:Sometimes but *not always* these extra degrees of freedom look like compactified coordinates of some higher dimensional spacetime, and then it is often useful to visualize them in terms of higher dimensions.
MTd2 said:Not always, how?
MTd2 said:I see, so the different string theories are like generalized Fourier transforms. In the usual Quantum Mechanics, you just transform between momentum and position, in string theory you transform between several different types of basis, which are the different string theories. Right?
MTd2 said:Besides that, is there anything that forbids an operator on the worldsheet that exchange chiralities?
MTd2 said:What is missing to define an M-Theory nowadays?
suprised said:The feat would be to formulate something that gives rise to all those field, string and membrane theories when expanded around the relevant regions of the vacuum parameter space, in terms of the appropriate degrees of freedom.
MTd2 said:Would you mind citing some things that are known not to be reproduced "when expanded around the relevant regions of the vacuum parameter space" ?
suprised said:Well for example sick QFT with gauge anomalies.
MTd2 said:Isn't that a good thing? Why should M-Theory include them?
suprised said:Yes it is a good thing... M-Theory supposedly is the mother of all consistent theories...and if I may say something provocative, IMHO it is defined by this property.
MTd2 said:OK, then. I thought you said that there were consistent theories that were not reproduced "when expanded around the relevant regions of the vacuum parameter space". Hmm, but what I actually mean, if it is that they can be reproduced right now? If there is any, can you tell me which one is?
suprised said:.. don't understand the question...;-(
MTd2 said:Well, you know that the final form of m-theory is not known. How can you that something is missing?
MTd2 said:Well, so M-Theory is a gut feeling?
MTd2 said:What do you think of E8 Gauge theory? (the one in 12 dimensions, not the Garrett Lisi's).
suprised said:Well it is a bit more than that, you can't press complicated matters in such a simple buzzword ;-)
suprised said:Which E8 gauge theory in 12d? I never heard of it...
MTd2 said:So, suprised, what did you think of E8 gauge theory? Witten invented it, but there is not that many citations within 12-9 years since it was invented, as it usually happens when he comes up with breakthrougs. Perhaps people are overlooking it? What do you think?
suprised said:The paper mainly deals which mathematical/technical questions of anomalies and other aspects of the M-theory partition function, it is very dense and I cannot tell much more without carefully reading it, but why do you put so much emphasis on that?
MTd2 said:Because it has 12 dimensions, like F-Theory. It is even shown in a later paper that it is dual to it. But the reason that, unlike F-Theory, there is a certain "bulk" which is not supersymmetric, in fact, supersymmetry is a lower energy condition on the 11th dimension border. I read an explanation of this in another paper that explains it. Unfortunantely, I cannot post it here.
suprised said:In fact the role of K-theory in string physics is somewhat overrated and doesn't play an important role beyond cohomology, so I would advise anybody not to waste time by studying papers on K-theory, unless she really wants to understand subtleties in defining D-brane charges and similar.
MTd2 said:It was later argued that K-Theory is not enough, you have to consider elliptic-cohomology, which is one step further in complexity, since it deals with curves on a torus, or lattice. According to what I sent you, K-theory cannot classify 3-form fields with torsion.
And if I don't classify what the fields are, how can I find what is m-theory?
suprised said:Well I have seen claims but right now I don't know of any concrete use of elliptic cohomology in M-theory. It sounds more like a wish list for math concepts to be applied somewhere in physics (and yes, there are plenty). I studied a few papers of Sati *et al* but really couldn't get anywhere.