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D-branes are not restricted to planar geometries. They can take on many different forms, and you often encounter branes wrapped around spherical manifolds, like $S^1$ or $S^4$. To determine whether a given configuration is stable, you have to evaluate the action of the D-brane configuration, which is given by the Dirac-Born-Infeld action. For a $Dp$-brane, ...

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After you will learn more about spinors, you will see that all spinors belong to $\left(\frac{1}{2}, 0\right) + \left( 0, \frac{1}{2}\right)$ representation of $SL(2,C)$ group. Spinorial equations allow to extract Lorentz-invariant subspaces in the overall space of $\left(\frac{1}{2}, 0\right) + \left( 0, \frac{1}{2}\right)$ representation. Both Dirac and ...

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Recall a Dirac spinor which obeys the Dirac Lagrangian $$\mathcal{L} = \bar{\psi}(i\gamma^{\mu}\partial_\mu -m)\psi.$$ The Dirac spinor is a four-component spinor, but may be decomposed into a pair of two-component spinors, i.e. we propose $$\psi = (u_{+},u_{-})^{T},$$ and the Dirac Lagrangian becomes, $$\mathcal{L} = ... 0 The counting of the dimensions is the same for D1-branes and the fundamental F1-strings. There are 24 physical scalars because the embedding of a 2-dimensional world sheet (of either F-string or D-string) may be locally specified by 24 functions. For example, as long as the coordinates X^0,X^1 are changing at least "a little bit" in a region of the world ... 3 The connection of superconductivity to Seiberg-Witten theory can be understood through the observation that superconductivity is related to the Meissner effect, which is the exclusion of magnetic field lines from a superconductor. Seiberg-Witten theory is based on the analysis of the moduli space of an \mathcal{N}=2 supersymmetric Yang-Mills theory. It ... 1 Saying that a splitting varies over the moduli space is not completely well defined: you have to say how to identify the total spaces at different points of the moduli i.e. to specify a flat connection on the bundle of total spaces. In the B-model, if you take the Gauss-Manin connection as the flat connection then the Hodge splitting varies over the moduli ... 2 The conformal group is defined for any spacetime you want. The conformal group of d-dimensional Euclidean space, which has isometry group SO(d), is SO(d+1,1). The conformal group of d+1 dimensional Minkowski space, whose isometry group is SO(d,1), is SO(d+1,2). The defining property of the conformal group is that its the set of transformations that leave the ... 0 My answer to this question may seem very simple but it's the basic. Density=Mass/Volume as you know an infinitesimally small particle will have infinitesimally small mass and volume.That means your numerator and denominator both are approaching to zero (but not exactly zero) so in that case you will have to apply limit (as for 0/0 form) to get density which ... 1 The solution is called Quantum Mechanics . Physics is the discipline of modeling measurements ( called data) with mathematical theories. By the nature of modeling there are limits of application. In the beginning of the modern physics era when the beautiful theories of Classical Mechanics, Thermodynamics and Electromagnetism were first proposed with ... 1 It was shown by Zumino (Supersymmetry and Kahler Manifolds Phys.Lett. B87 (1979) 203 ) that the supersymmetric non-linear sigma model in four-dimensions (with target M) necessarily requires the manifold, M, to be Kahler. A dimensional reduction of this model leads to a two-dimensional nonlinear sigma model with (2,2) supersymmetry. (See also: B. ... 1 I don't think it's a bad question. I think as the comment says, the answer is yes, many Universes may have similar properties. However, it has been argued that our Universe's cosmological constant is finetuned, and that this fine tuning has an environmental explanation. I.e., our constant is untypical, but since observers need e.g. structure in their ... 0 The original reference for the derivation of this result is http://arxiv.org/abs/hep-th/9302047. A brief answer to your questions is: the Euler density in generic number of dimensions is a diffeo-invariant functional of the metric, built out of the curvature. In dimension 2d it is a polynomial of degree d in the Riemann tensor. Its defining property ... 4 I) The string (target space) coordinates X^{\mu}(\tau_E,\sigma) depend on a (world sheet) spatial coordinate \sigma and a (world sheet) temporal coordinate \tau_E (which we here have Wick-rotated to Euclidean time, hence the subscript E). II) Similar to how one quantizes a field in QFT, in string theory, the Fourier series expansion of string ... 3 I'll add a small disclaimer as well, I am a mathy with little to no physics background, so if any of the below needs expanding, feel free to ask! (Though I'll mention that I felt a lot more comfortable with this stuff when I first computed the induced actions I'll mention below and really got my hands dirty verifying everything.) To see that there is only ... 0 The main point is that the operator-state correspondence maps all the annihilation operators to zero, so that an operator-valued Laurent series in z and \bar{z} maps to a ket-state-valued power series in z and \bar{z}. 0 Disclaimer: I've never read this particular book, but I'm reasonably certain index notation is invariant across most of physics. The mathematical notion of interest is of course the inner product in some, well, inner product space. The definition of an inner product is given by a bilinear form - the metric. Let's call it g. Then$$ (a, b) \equiv g(a, ...

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String theories respect symmetries of the 4d Poincare group, including those that result in special relativity. As such, faster than light particles are expected to be absent in nature, if string theory is correct.

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The way we measure length is to use the metric tensor. Any spacetime has a metric tensor associated with it, and it's the metric tensor that is responsible for the notion of distance. To make this a little less abstract consider a concrete example. In flat spacetime the metric tensor is just: $$ds^2 = -c^2dt^2 + dx^2 + dy^2 + dx^2$$ Suppose you want to ...

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I'm not an expert on this particular topic, but I believe I can answer your question. There are different kinds of "dimensions". The standard 3 spatial dimensions we live in are infinite in extent. However, one can also imagine dimensions that have a periodicity (like a circle). In such cases, there is a "size" to the dimension that refers to the ...

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I'm no expert on the subject, but according to one of the proponents of this model (http://wwwphy.princeton.edu/~steinh/npr/), the 2 branes "stick" to create the universe. Hope that helps.

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