I often see people researching (2+1)-Gravitational theories such as Chern-Simons. Why is it interesting or what's the motivation underlying that study if there are 4 macroscopic dimensions?
123146
The last decades there has been a lot of research going on in the the area of three dimensional gravity. The motivation, I understand, is threefold:   Whereas gravity is not perturbatively renormalizable in four spacetime dimensions, in three dimensions it is. To make it even more interesting it has black hole solutions and it is exactly solvable. This opens the way to to study quantum black holes. This make three dimensional gravity a very interesting system on itself. Through the AdS/CFT correspondence there is a connection between conformal field theories (CFT) in two dimensions and gravity in three dimensions. CFT's are important in condensed matter physics and one can use 3D gravity to learn more about them. Gravity in three dimensions is simpler to deal with then gravity in four dimensions. Therefor it can be used as a toy model for gravity in four dimensions.    I am wondering what are the most important insights that 3d gravity brought in these respects? In particular I am interested in point three: did 3d gravity provide any new view on 4d gravity so far?
53634
I am a first year PhD student in theoretical physics with a background in QFT (up until relativistic fields, path integrals and gauge theories and anomalies) and some algebraic topology but my understanding of anomalies is weak and I am looking for references for discrete anomalies or anomalies in general. Any textbooks/papers that could be useful are appreciated.
20711
I am in the last year of MSc. and would like to read string theory. I have the Zwiebach Book, but along with it what other advanced book can be followed, which can be a complimentary to Zwiebach. I would like a more mathematically rigorous book or lecture notes along with Zwiebach.   Specifically, mention whether the book discusses string theory   Rigorously? Intuitively?   What's the scope of the book? Does it cover the advanced materials, e.g. Matrix string theory, F-theory, string field theory, etc. Maybe even String Phenomenology?
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What I am interested to see are specific examples/reasons why gravity should be quantized. Something more than "well, everything else is, so why not gravity too". For example, isn't it possible that a quantum field theory on curved space-time would be the way treat QFT and gravity in questions where the effects of neither can be ignored?
48662
I have some questions with string theory:   Why is it that there is exactly 4 large spacetime dimensions while the rest remain small? It is a nonlocal QFT. How could that fit in GR?
66087
Emphasis is on the irreducible. I get what's special about them. But is there some principle that I'm missing, that says it can only be irreducible representations? Or is it just 'more beautiful' and usually the first thing people tried?   Whenever I'm reading about some GUT ($SU(5)$, $SO(10)$, you name it) people usually consider some irreducible rep as a candidate field. Also, the SM Lagrangian is constructed in this way. (Here, experimental evidence of course suggests it.)
110734
Since I studied General Relativity I had this question running on my mind. As I see it (just taking lectures of Quantum Field Theory right now)  "Why you need a gauge boson for gravity when the higgs brings things mass?"  You know, mass is the cause for physicist to study differential geometry so why we need another unproven particle, to exist, in order to describe it?
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Let's say that we want to measure the gravity force in 1D, 2D, 3D  and higher spatial dimensions.   Will we get the same force strength in the first 3 dimensions and then it will go up? How about if we do this with Electromagnetic force?   I've include the Electromagnetic force just to see if I can find an analogy to the gravity force behavior.
61319
We consciously know and feel the first three dimensions and with some thinking time as well. But according to literature like String theory etc., we have many many more dimensions. We can readily express them in paper. But why can't we realize them? Why can't we experience them like the first three dimensions?  PS. I was pondering on this when I saw the movie Interstellar where even the fourth dimension 'time' is expressed using the first three dimensions for Cooper. PPS. The first three dimesnions being the X, Y and Z axes.
112539
String theorists say that there are many more dimensions out there, but they are too small to be detected.    However, I do not understand why there are ten dimensions and not just any other number?  Also, if all the other dimensions are so coiled up in such a tiny space, how do we distinguish one dimension from the other?  If so, how do we define dimension?
51270
I think I've missed this point somehow. I've just started with Compactification and so far, I don't really see why it is restricted to the above mentioned types of manifolds?   I have to admit, when studying T-Duality, I simply took Toroidal compactification as a kind of "why not"-thing.  Could someone point me in the right direction? Been skipping through my books to look for some explanation of this, but couldn't find anything. Thanks!
12198
I'm a layman, but i watched some intereting videos about big bang on youtube[michio kaku, hawking this kind of things, not some crackpots :)]   I described everything on my picture:     So is there any possibility to see that inner side, for example, by creating wormhole, or entering new dimension? Or i get something wrong, on the way, and my model is totally wrong?  And another question. I heard that even if you would fly a ship across the universe you would eventually end in the place where you started, because we live in a 3d space that is defined on a surface of big sphere. But why a big sphere? Universe might be a big mobius strip, and the same principle of ending at start will apply. Is it possible?  Thanks in advance, and please don't bash me for silly questions. Im just curious, but i don't have any degree in physics. Im also not an english native speaker.
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I'm interested in learning how to use geometry and topology in physics. Could anyone recommend a book that covers these topics, preferably with some proofs, physical applications, and emphasis on geometrical intuition? I've taken an introductory course in real analysis but no other higher math.
83550
One way that I've seen to sort-of motivate string theory is to 'generalize' the relativistic point particle action, resulting in the .  However, once you see how to make this 'generalization', it becomes obvious how to write down the action, not just for a string, but for manifolds of higher dimension as well.  In fact, Becker-Becker-Schwarz (the main source I happen to be learning from) actually do this.  But (as far as I have read), they merely write down the action and do nothing further with it.  My question is:  what happens when we proceed along the same lines as string theory, but when replacing a string with a 2-manifold, the simplest example of which would be the 2-sphere, a "shell/membrane"?  Assuming 3 spatial dimensions, this is the highest dimensional manifold we can consider (because we don't allow for non-compact manifolds).  Furthermore, there is only one compact manifold of dimension 1; however, there are infinitely many compact manifolds of dimension 2, which could potentially make the theory much richer (and probably much more difficult).  For example, in string theory, we are stuck with $S^1$ (if you insist upon having no boundaries), but if you allow for 2 dimensions, we could consider the sphere, the torus, etc.  Because it seems that this path is not ever presented (in fact, I've never even heard of it), I would presume that something goes wrong.  So then, what exactly does go wrong?
69072
Can someone please give me the prerequisites and mathematics required for string theory? Are there some good references to study it, both online and in a book? Please consider I am a newbie in string theory, and only about up to the level explained in Hawking's Brief History of Time and Penrose's Road to Reality. I would prefer something which does not omit rigor, but builds it up.Also, are there good online lectures on this?  (I have covered most of GR, but I am not really comfortable with advanced Quantum mechanics. I have studied QM only from Griffith's book, and a few McGraw hill lecture notes.)
38709
What is the exact shape of the universe? I know of the balloon analogy, and the bread with raisins in it. These clarify some points, like how the universe can have no centre, and how it can expand equally everywhere in all directions. But they also raise some questions, like if you are on the surface of a balloon and travel in 1 direction, you will eventually return to your starting point, is it possible our universe have this feature?  If it has, or had, would this be a symmetry of sorts ($\psi(x)=\psi(x+R)$), and as such have a conserved quantity associated with it (by Noether)? Assuming "small curled up dimensions" wouldn't these dimensions have this type of symmetry, what are the associated conserved quantities? Is it known exactly what the geometrical shape of the universe is? (on a large scale) (I am not talking about only the observable universe). How does one define the "size" of a dimension, is this scale only applicable to curled up ones? Is it possible to describe to a layman the shape of the universe without resorting to inept analogies?
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Since there are  complex numbers (2 dimensions) and quaternions (4 dimensions), it follows intuitively that there ought to be something in between for 3 dimensions ("triernions").   Yet no one uses these. Why is this?