I come aross an OPE between stress tensor components in CFT which is  \begin{equation} T(z)\bar{T}(\bar{w})\sim -\frac{\pi c}{12}\partial_{z}\partial_{\bar{w}}\delta^{(2)}(z-w)+... \end{equation} I am confused about this OPE. Because in general in CFT chial part does not correlated with anti-chiral part, for example in free fermion and boson. So how to derive this OPE?
In his lectures on String Theory (), Tong gives a proof of the Weyl anomaly, using equation $(4.36)$. It seems wrong to me.  Here he uses the OPE between the stress-energy tensors $T_{zz}T_{ww}$  obtained when trace vanishes, i.e. $T_{z \bar{z}} = 0$: this implies that they are holomorphic functions $T_{zz} = T_{zz}(z)$. But in this proof he starts from the fact that $T_{z \bar{z}} \neq 0$ (we want to proof this thing after all) and so $T_{zz}$ is not a holomorphic function anymore! In the OPE $(4.36)$ I should have also terms with $(\bar{z}- \bar{w})$.  I can't also understand why he uses in the rest of the proof only the singular term $(z-w)^{-4}$, neglecting the other ones $(z-w)^{-2}$, $(z-w)^{-1}$.  (The same proof is given in these lectures  on conformal field theory, equation $(6.9)$).  I'll be really thankful if someone could explain me this proof :)
I installed Blender from official Ubuntu repository but its version is always behind the version available from the official Blender website.  I'm aware that I can launch the program within the downloaded folder, but i want to replace the install version with a new version downloaded from the website?   It must be present in the unity launcher.  I'm also aware of the available PPA's that are available, however I just want to install Blender manually.  Thanks in advance How do I completly remove XP from my pc. I currently have a dual boot with XP and Windows 7. Since installing Windows 7, I have never used XP. Can I remove it without causing problems with Windows 7? How many numbers of 6 digits, that can be formed with digits 2,3,9. And also divided by 3? How many numbers of 6 digits, that can be formed with digits 2,3,9. And also divided by 3?  $$$$ I was trying to to add 2^6 (when there is no 2)+ C(6,2)2^2 (when 2 can be in two places)+C(6,3)2^3 (when 2 can be in three places)... 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Similar to the current &quot;Related Questions&quot; feature, this could be used to answer otherwise-unanswerable questions before they're asked, thus saving everyone time and frustration. I propose a simple system whereby a web cam is aimed at an ordinary  device, long recognized as one of the most accessible and accurate fortune-telling mechanisms available to modern society. A simple  could be placed under this rig and triggered in response to the user's typing. Once focus leaves the Title input field, a short delay will be triggered, followed by a bit of logic to capture the 8-ball's result and feed it through a simple OCR routine to produce the result.  So far as I'm aware, SO would be the first major Q&amp;A site to implement such a feature...  Examples:            ...another UV resurrection... How to pass arguments to addEventListener listener function? 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Basically a proof of how it is always true. Why the default eth0 interface is down by default on CentOS? How do I get the member to which my custom attribute was applied? Pretty much the problem asks if a function is continuous at the point $c$ and $f(c) &gt; 0$ then there exists a $d &gt; 0$ such that $\forall x$, $f(x) &gt; 0$ with $|x-c| &lt; d$.   I can understand what the problem means. That if a function is positive at a point then there is another point that's really close that'll also be positive. I can not prove this in a formal way though. I've tried using the intermediate value theorem and I do not know hot to implement it. Any ideas? Proving Cauchy condensation test Unless I missed something key during Descent 1/2, how is it that the Borg are once again a collective? Is JavaScript a pass-by-reference or pass-by-value language? I'm trying to show that $R = \mathbb{Q}[X,Y]/(Y^2-X^3)$ is not a UFD, but I got stuck.  To prove this, I could try to find two "different" factorisations for one element, but I am not familiar with this, so I tried to use a lemma and one of the previous exercises. If my syllabus is right, in every UFD counts $$ x \ \text{is irreducible} \quad \iff \quad x \ \text{is prime}$$ My syllabus also states that the elements $\bar{X}, \bar{Y} \in R$ are irreducible. So I tried to show that at least one of the elements $\bar{X}, \bar{Y} \in R$ does not generate a prime ideal.  This would mean that I should find two polynomials $f,g \in \mathbb{Q}[X,Y]$, such that  $$\exists p \in \mathbb{Q}[X,Y], \quad fg - pX \in (Y^2-X^3)$$ and $$\forall q \in \mathbb{Q}[X,Y], \quad f-qX \notin (Y^2-X^3) \ \wedge \ g-qX \notin(Y^2-X^3)$$ or the same thing but then for $Y$.  I hope that you can tell me if this approach is correct, and provide me a hint. I'd appreciate it if you told me the solution, but please start your answer with a hint, clearly separated from the rest. What is the easiest way to strip a desktop edition to a server edition? We have installed Ubuntu desktop edition on our development server. Now that we have it in a data center we would like to strip it down to a server edition.  Is there an easy way of doing so rather than just going in and uninstalling packages by hand? Here's the context       "Her heart leaping into her throat, she tiptoed into the salon. Such was her astonishment at seeing Mike chatting with her boss that she leaned against the wall, incapable of making another move."   Is this a phrase or what? Could it be used in other forms as well? When looking at a PDF document I often want to zoom-out to scroll quickly to its contents and get an overview.  However, when I zoom-out past a certain threshold (it seems to differ per PDF) Safari thinks I want to see the tab overview:    I have never found a use for this function, so it only causes annoyance.  Can I turn this tab overview off somehow? A solution that uncouples the pinch-to-zoom gesture from the functionality would also work.  I'm on Mountain Lion 10.8.5 with Safari 6.1.3. Libvirt: how to pass qemu command line args? I have the current libvirt 1.2.20 i want to pass to my machine create with virt-manager some qemu flags. I edited the file and add    &lt;/devices&gt;   &lt;qemu:commandline&gt;           &lt;qemu:arg value='-L pc-bios'/&gt;   &lt;/qemu:commandline&gt; &lt;/domain&gt;   But doesn't work i also tried to edit from virsh  virsh edit domain   and put   &lt;qemu:commandline&gt;           &lt;qemu:arg value='-L pc-bios'/&gt;   &lt;/qemu:commandline&gt;   But give me this error  errore: XML document failed to validate against schema: Unable to validate doc against /usr/share/libvirt/schemas/domain.rng Element domain has extra content: qemu:commandline  Failed. Try again? [y,n,i,f,?]:    How to pass correctly qemu command line? Thanks