New answers tagged

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Worldsheet supersymmetry is the fermionic symmetry of the worldsheet RNS action under the worldsheet supsresymmetry transformations that look like $$ \sqrt{\frac{2}{\alpha'}}X \mapsto \sqrt{\frac{2}{\alpha'}}X + \mathrm{i}\bar{\epsilon}\psi^\mu$$ and which I'm too lazy to type out for all fields (and which also depend on whether or not we're looking at the ...


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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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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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As you said in your question, quantum field theory is very important; it takes the ideas of quantum mechanics and applies them to fields, such as the electromagnetic force (in fact, quantum electrodynamics was the beginning of quantum field theory). Quantum field theory has plenty of evidence to support it, and it is still an ongoing work. String theory, ...


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According to the abstract of a paper at https://arxiv.org/abs/hep-th/0604072, Breakdown of local physics in string theory at distances longer than the string scale is investigated. Such nonlocality would be expected to be visible in ultrahigh-energy scattering. The results of various approaches to such scattering are collected and examined. No evidence ...


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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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I think there are a number of generalizations. The first is the partition function should be considered quantum mechanically. The reason is that spacetime can contribute to entropy, such as with Hawking radiation. To start the partition function is the trace $$ Z[\phi] = \sum_n\langle\phi_n|e^{-H(\phi)\beta}|\phi_n\rangle $$ Now, if one is interested in the ...


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The particle is not larger nor more massive. We normally describe particles using quantum field theory, and in QFT particles do not have a size. This is discussed in the answers to Why do physicists believe that particles are pointlike? and it would be worth reading through them. To say that a particle is a point is a bit of an over simplification. We ...


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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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String theory postulates that of the elementary particles we currently know about, each relates directly to low-energy string vibrations, the presence of multiple holes causes the string patterns to fall into families. Each hole in the Calabi-Yau space is a group of low-energy string vibrational patterns. If the C-Y has three holes, then three families 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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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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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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The string action $$ S_p = -T\int d\tau d\sigma (-\gamma)\gamma^{ab}g_{\mu\nu}\partial_aX^\mu\partial_bX^\nu, $$ or Poyakov action, is evaluated in a path integral $Z = \int{\cal D}[X]e^{-iS}$, or defines states $$ |\psi\rangle = \int{\cal D}[X]e^{-iS}|n\rangle $$ on a Fock basis. In the light cone gauge, $X^\pm = \frac{1}{2}(X^0\pm X^i)$ the Hamiltonian ...


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Of course they can. Some particles arent elementary, imagine Glueballs Neutrons, Protons, they all conclude other particles. But an elementary particle (electron, quark, so on..) are described by one single string. It is also important, what particles you are talking about, because there exist open and closed strings, which all have other mathematical ...


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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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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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Your derivation is close. The Polyakov action is $$ S[X,\gamma] = T\int d\tau\int d\sigma (-\gamma)^{1/2}\gamma^{ab}\partial_aX^\mu \partial_bX_\mu, $$ for $T = -(4\pi\alpha')^{-1}$. The variation with respect to the string $X_\mu$ then gives $$ \frac{\delta S}{\delta X^\mu} = T\int d\tau\int d\sigma\left[\frac{\delta}{\delta X^\mu}\left((-\gamma)^{1/2}\...


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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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