# Tag Info

## Hot answers tagged string-theory

3

Consider two vector fields $a^\mu(x)$ and $b^\mu(x)$ in a space-time. The local angle between the two vector fields is given by $$\cos\theta(x) = \frac{ a(x) \cdot b(x) }{ \|a(x)\| \|b(x)\| } = \frac{ g_{\mu\nu}(x) a^\mu(x) b^\nu(x) }{ \left| g_{\alpha\beta} a^\alpha(x) a^\beta(x) \right|^{\frac{1}{2}} \left| g_{\rho\sigma} (x) b^\rho(x) b^\sigma(x) ... 3 This started as a comment in reply to CuriousOne's comments, but is getting too long , so I will answer the question if it does not become duplicate. Observations are the basic definition of "real" in physics, as with life in general. Observations start from classical particles, and in the last centuries a consistent mathematical model of mechanics, ... 1 M2 and M5 branes are fundamental objects of M-theory. You can see this from the superalgebra of D=11 SUGRA, which is the low energy limit of M-theory. Moreover M2 and M5 couple respectively electrically and magnetically to the RR 3-form A_3 of D=11 SUGRA. In the compactification limit for the eleventh dimension, from M-theory you get the IIA ... 1 I) It seems the resolution to OP's question lies in the difference between the Levi-Civita symbol, which is not a tensor and whose values are only 0 and \pm 1; and the Levi-Civita tensor, whose definition differs from the Levi-Civita symbol by a factor of \sqrt{|\det(g_{\mu\nu})|}. II) The 2D Euler-density is$$ E_2~=~ \frac{1}{8\pi} ...

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There are no fundamental strings in M-theory. M2 branes can end on M5 branes and these appear as strings in the world volume of the M5 branes but these strings are of solitonic nature.

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Since the worldsheet theory is conformal, you are allowed to "shrink the boundaries to a point". So the usual viewpoint is that the worldsheet are boundary-less with certain points on them corresponding to the former boundaries. The cylinder, for instance, becomes a twice-punctured sphere - the punctures are the places where one inserts the vertex operators ...

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To my knowledge it is not forbidden by the standard model laws. The point is that at low energy scale this process is strongly subleading with respect to other decay's channels, for instance to an electromagnetic decay in two photons. At high energy the strength of gravitational force grow and that process could be one of the main channels of decay. To be ...

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You want to take the derivative with respect to both z and w. Take $${X^\mu }\left( z \right){X^\nu }\left( w \right) \sim - {1 \over 4}{\eta ^{\mu \nu }}\ln \left( {z - w} \right)$$ and use the following derivative {{{\partial ^2}} \over {\partial w\partial z}}\left[ {{X^\mu }\left( z \right){X^\nu }\left( w \right)} \right] = {\partial \over ...

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There is nothing to add to the first part of Jake Lebovic's answer. With regard to the second part of the question -- how to compute the OPE of two stress tensors -- one uses Wick's theorem. Normal ordering means one does not contract together the individual fields making up the normal ordered operator, in this case the two $\partial X$'s making up ...

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