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Given the four point function $\langle \phi(x_1)\phi(x_2)\phi(x_3)\phi(x_4)\rangle$, the conformal block expansion depends on what operators you replace by the OPE. So if you insert the OPE for $\phi(x_1)\phi(x_2)$ and the OPE for $\phi(x_3)\phi(x_4)$ then this corresponds to the s channel---one can also call this the (12)(34) channel---.. The t channel is ...

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It depends on the context whether M-theory refers to the full UV completion or just the 11D supergravity limit. For example when people say "type IIA string theory is related to M-theory by T-duality" and go on to calculate something in "M-theory", they really mean the supergravity limit. However, when you hear vague statements like "M-theory is the ...

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A fundamental string is the basic building block when we are talking about string theory: a one-dimensional object that may vibrate, and whose states of excitation correspond to particles. These strings may split and merge, just as particles may decay and annihilate to form a new kind of particle. As there are both open and closed strings, it turns out that ...

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Instead of integrating over the region in moduli space where $\Im(\tau) \to 0$ (corresponding to the UV limit), we can perform a modular transformation and integrate over the region where $\Im(\tau) \to \infty$ (corresponding to the IR limit). I think that's all he wants to say, there is (as far as I understand it) nothing deeper behind it. But it is not ...

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A guitar pickup generally produces an electrical signal representative of the motion of the string. Below is a diagram showing the motion of a string for the first several harmonics: As you can see, the even-numbered harmonics have a node (a point where the string doesn't move at all) at the midway point, and the odd harmonics don't. When you pluck a ...

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Extra dimensions in general have to be compact, since a four-dimensional description fits the world we perceive and measure (so far) very well. It is this compactness that sets a length scale. Usually, we assume that the four "regular" space-time dimensions are not compact, i.e. extended infinitely. In higher dimensions concepts like angular momentum, ...

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What is the process, the rule or the method which leads me to understand/calculate the size of these extra dimensions? How can I understand or prove that, taking the String example, the additional dimensions are so small? Where does the number of their magnitude come from? At the present moment we have no experimental evidence that there exist the extra ...

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Historically this has always been the problem with the Kaluza-Klein approach. In the original Kaluza-Klein theory there was no mechanism to determine the scale of the compactified dimension, and indeed one of the criticisms of it was that the compact dimension was unstable and would naturally expand to infinity. In the context of string theory the problem ...

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When Brian Greene talks about the shape of the extra dimensions he is using a simple word for some exceedingly complicated mathematics. For example suppose you are trying to compactify just two dimensions - call them $x$ and $y$ for convenience. Compactifying the dimensions means forming them into a loop, but starting from a flat sheet you could loop the two ...

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According to Brian Greene it is possible to calculate the physical constants from the shape of the extra dimensions. This isn't scientific fact I'm afraid. It's perhaps presented as such, but there's absolutely no evidence for string theory, and hasn't been for fifty years. Is it possible to do the inverse, so predict the shape of these dimensions ...

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As far as I know, this is an open question. The technical name is the problem of "moduli stabilization" in string theory, because there some fields (called moduli) the values of which determine the size of the dimensions. The problem is that string models are consistent for a big range of these values, so indeed, it could have been that all directions are ...

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I found the answer to my question in this publication: http://arxiv.org/pdf/hep-ph/0309075v2.pdf The mass formula is given by $$m = \sqrt{\frac{2m_1m_2}{\alpha}J+(m_1^2 + m_2^2)},$$ where $m_1$ and $m_2$ are the masses of the partons, $\alpha$ is the fine structure constant and $J$ is the angular momentum of the hadron.

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What came to be called "discrete torsion" is simply the data that makes the B-field gerbe be equivariant over the orbifold. This was clarified by Eric Sharpe, see the references here: Eric Sharpe, Discrete Torsion and Gerbes I (arXiv:hep-th/9909108) Discrete Torsion and Gerbes II (arXiv:hep-th/9909120) Discrete Torsion, Quotient Stacks, and String ...

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I would guess that you're thinking of the brane world ideas. If so, the branes you're describing are not eleven dimensional. They are surfaces of dimension lower than eleven embedded in the eleven dimensional space. For example in this context example our universe would be a four dimensional brane.

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