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In the presence of orientifold planes, every object (away from the orientifold fixed points) including a D-brane has "two copies". So it's a matter of convention whether this pair of copies is counted as "one D-brane" or "two D-branes". Because the whole half-space is a "copy" of the other one, it makes sense to only consider one-half of the space as "the ...

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A p-cycle is a differential form that lives in $ker(\partial_p)$ for the differential $\partial_p$ (in grading $p$), and such a form is nontrivial if it is not in the image of $\partial_{p+1}$. Mathematically we can see this as a cycle that is not the boundary of anything, picture a circle around a torus that bounds no area on the torus. If one has a ...

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I do not know almost anything about string theory, but I can say something from the general quantum theory viewpoint. First of all you stated Malament's theorem hypotheses into a not very precise form. The sets $\Delta$ are assumed to be subsets of a 3D spacelike surface $\Sigma$ (the rest space of an observer) whereas $a$ in the third requirement is a ...

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While writers like Briane Green do a generally laudable job of trying to explain string theory at a popular level you need to appreciate that this always involves gross simplifications. The reality is that string theory is horrifically more complicated than the pop science explanation suggests. To properly explain how particles arise in string theory is ...

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According to the fuzzball proposal in string theory, black hole are actually horizonless and regular solutions. For some systems in five dimensions made with bound states of intersecting branes this has been already proved directly in supergravity: there are solutions without horizons and singularities, with the same asymptotic charges (Mass, Angular ...

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At best things are pretty speculative. Cumrun Vafa has proposed that black holes have condensates of tachyons. In some sense you can understand this without much complexity. The Schwarzschild metric has a physical singularity that is a spatial surface. The Penrose conformal diagram for the Schwarzschild metric illustrates this The bosonic string has two ...

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Confinement is a low energy phenomenon. By this I mean that as you increase the energy with which you probe the properties of quarks they appear more and more like free particles. This property is called asymptotic freedom. If we had some hypothetical accelerator capable of doing experiments at energies where stringy effects start to be significant it would ...

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A more "pedestrian" application is that the low-energy physics of a Heisenberg antiferromagnetic spin chain is described by a WZW theory. This is a very simple and concrete model which has been shown to accurately describe many real materials. See for example http://arxiv.org/abs/hep-th/9802014v1, http://arxiv.org/abs/1211.5421v1, or section 7.10 of ...

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This is not really an answer (the answer is ACuriousMind's comment: this is a double coset space), but it may help to consider the construction of the moduli space of elliptic curves, as this can be done in the same way but is very easy. Every complex elliptic curve is obtained as $\Bbb C$ modulo a lattice. Scaling the lattice by a complex number gives an ...

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There are two things going on. One is modulo that is the forwards slash / and the other is set-minus $\setminus$ the backwards slash. The $$G_4(20) = \frac{O(4,20)}{O(4)\times O(20)}$$ is the Grassmanian space defined by $4$-planes. the group $O(\Gamma_{4,20})$ is an orthogonal group over the unimodular transformations, a bit like saying $O(n,\mathbb Z)$, ...

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Here, a term spin should be understood as a quantum number you get after doing dimensional reduction of a higher dimensional theory to (1+3)-dimensions. If you follow this assumption, you find a spin of Kalb-Ramond field is 1. I think most people have this in mind, when they say a spin in higher dimensions. In general, you get more quantum numbers than you ...

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In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. It describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, ...

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The heterotic group decomposes as $E_8~\rightarrow~SU(3)\times E_6$, The $\bf 248$ of the $E_8$ decomposes as $${\bf 248}~\rightarrow~(\bf 8,~\bf 1) + (\bf 1,~\bf 78) + (\bf 3,~\bf 27) + (\bf\bar 3,~\bf\bar{27})$$ We have here the $(\bf 8,~\bf 1)$ of $SU(3)$ which is identical in form to the irreducible representation used for gluons, or the old nonet ...

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I am going to offer a small bone here. I am somewhat interested in the role of Taub-NUT spacetimes, and so contributing will help me to track this in order to read other contributions. Thanks for the Gubser paper. From a more physical perspective I will just throw out something with magnetic monopoles, which are related to Taub-NUT spacetimes that have a ...

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One has to keep clearly in mind the structure of present day physics. Quantum mechanics is the theory that started as non relativistic with the Schrodinger equation for potentials, and became relativistic with the Dirac and Klein Gordon and quantized Maxwwell equations. Quantum mechanics has postulates which used with the solutions of the differential ...

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