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33

When lasers cut something, they're only cutting in the sense that they're making atoms be not as attracted as they once were to each other. When you get down to the nitty-gritty details, it is not really the same as mechanical cutting. Remember that lasers shoot photons, and when photons hit atoms, they excite electrons. If you excite these electrons ...


18

Duality is the relationship between two entities that are claimed to be fundamentally equally important or legitimate as features of the underlying object. The precise definition of a "duality" depends on the context. For example, in string theory, a duality relates two seemingly inequivalent descriptions of a physical system whose physical consequences, ...


13

Cutting is a process when you deliver energy to break chemical bonds in material that you cut. When you use a saw, you deliver mechanical (kinetic) energy that converts into kinetic energy of particles of the thing you cut, so they can get out of the thing. Laser is just another way to deliver such energy, since the a photon has enough energy to break some ...


12

Effectively, as the CERN website emphasizes The theories and discoveries of thousands of physicists over the past century have resulted in a remarkable insight into the fundamental structure of matter: everything in the universe is found to be made from twelve basic building blocks called fundamental particles, governed by four fundamental forces. It ...


10

Among normal books, Becker-Becker-Schwarz probably matches your summary most closely. However, you may want to look at a list of string theory books: http://motls.blogspot.com/2006/11/string-theory-textbooks.html Don't miss the "resource letter" linked at the bottom which is good for more specialized issues such as string field theory. An OK review of ...


9

This feels a little trivial, but I don't see why it isn't an example of what you want: Seiberg duality typically relates an $SU(N_c$) gauge theory with $N_f$ flavors to an $SU(N_f - N_c$) gauge theory. There are degenerate cases when $N_f - N_c = 1$ or $0$, which don't correspond to any dynamical gauge group in the infrared. These are usually described in ...


8

A list of some dual pairs for exceptional gauge groups is in Jacques Distler, Andreas Karch, N=1 Dualities for Exceptional Gauge Groups and Quantum Global Symmetries (arXiv:hep-th/9611088) For non-exceptional gauge groups there are "lists" in the form of explicit algorithms for how to construct the dual partner, see section 4 of Subir Mukhopadhyay, ...


8

A. The action of $N=4$ SYM (Super Yang-Mills theory) in $d=4$ is the simple dimensional reduction of the 9+1-dimensional SYM, the maximal dimensional SYM that exists. The latter is $$S = \int d^{10} x\mbox{ Tr } \left( -\frac{1}{4} F_{\mu\nu}F^{\mu \nu} + \overline{\psi}D_\mu \gamma^\mu \psi \right)$$ where $D$ is the covariant derivative and $\psi$ is a ...


8

Congratulations to your cute and solid paper and your new loophole that is morally on par with a loophole circumventing the Coleman-Mandula theorem itself – almost. ;-) I am confident you did the algebra correctly so let me offer you the form of the lore that I usually present and the way how you circumvented it. The lore says that the local fermionic ...


8

Think of the laser process as being similar to melting a substance through a change in state. An analogy might be putting a hot wire on top of an ice cube. It makes a 'slice' by heat, not by cutting. It turns the solid state ice into water and gas which doesn't hold together the same anymore.


8

M-theory compactified on a 2-torus is the same as M-theory compactified on a circle and then compactified on another circle because $T^2=S^1\times S^1$. M-theory compactified on a circle is type IIA string theory with $g_s$ being an increasing power of the radius of the compactified dimension. And if type IIA is compactified on a circle of a small radius, ...


7

One shouldn't imagine the T-duality between the two heterotic strings to be a $Z_2$ group, like in the case of type II string theories' T-duality. In type II string theory, there is only one relevant scalar field, the radius of the circle producing T-duality, and it gets reverted $R\to 1/R$ under T-duality. In the heterotic case, it's more complicated ...


6

Some people ascribe the duality to the duality between the classical appratus and the quantum microscropic system, but I think this is a little old-fasioned. The quantum description also works for a bad apparatus and a big apparatus--- like my eye looking at a mesoscopic metal ball with light shining on it. This situation does not measure the position of the ...


6

I think you will be less confused by the answers if you keep clearly in mind that wave equations are specific differential equations which apply to many classical systems which have been studied for over two centuries in great detail as they applied to light and sound and fluids. It so happened that the differential equations which first described the ...


6

Your question has many layers. The most comprehensive answer would have to explain everything about the gauge/gravity or AdS/CFT duality. Less ambitiously, there is a simple reason why a stack of D-branes behaves as a black p-brane. It carries a mass (well, the branes have a tension, the mass/energy density per unit volume), and if one has many D-branes, ...


5

AdS is not a manifold with boundary in the standard sense (where neighborhoods of the boundary are diffeomorphic to neighborhoods of points on the boundary of some Euclidean half space). The boundary to which people often refer in this context is the so-called conformal boundary obtained through a conformal compactification of the spacetime. In the ...


5

In his 1924 dissertation, de Broglie argued that matter particles should have a wavelength of $\lambda = h/p$, where $p$ is the momentum of the particle. The first confirmation of the diffraction formed by such matter waves was observed in the Davisson-Germer experiment: C. Davisson, L.H. Germer. Phys. Rev. 30 (1927) 705. Independently, G.P. Thomson (son of ...


5

"Any transformation that changes one theory into another" (or the same) theory is not called T-duality. It is just a "duality". A condition is that the two theories seemingly look different - otherwise the equivalence would be vacuous - but it must be true that their spectrum and the strength of interactions between their states must be totally isomorphic: ...


5

Let's consider the scattering of four (two to two) open strings, for the sake of concreteness. Using Feynman's approach to quantum mechanics in terms of the sum over histories, string theory commands us to compute the tree-level diagram as the sum over all histories – world sheets – where two initial open strings become two other open strings. By conformal ...


4

Concerning your "any compactification of bosonic strings", you are confused about the nature of dimensions we are compactifying. The non-chiral (having both left-moving and right-moving component) dimensions may be compactified on any lattice $\Gamma$ with $n$ dimensions. However, to compare with the heterotic strings, this (any) lattice $\Gamma$ should be ...


4

The duality has something to do with strength of interaction of a system with its environment, which may or may not consist largely of a piece of measurement apparatus of which we are consciously aware. In short, the duality arises from fixating on two extremes of behaviour: strongly coupling with the environment, or not. (Realizing this doesn't necessarily ...


4

Since S-duality relates a theory at weak coupling to a theory at strong coupling it is in general very hard to rigorously prove that two theories are dual. However, the basic arguments for why it should hold in string theory are given in many text books, see eg chapter 14 in Polchinski or Becker, Becker, Schwarz chapter 8. Here I will just sketch how the ...


4

Your question is one about true mathematical duality, you just do not know it. What you are looking for is Hodge duality, which holds in the exterior algebra of any vector space equipped with an inner product and an orientation, and the differential forms one looks at in EM, GR and elsewhere are just elements of the exterior algebra of the tangent space (or, ...


4

By analogy (between $\mathbf{E}$ and $\mathbf{B}$ as they are pretty much equivalent) then the divergeance of $\mathbf{B}$ field wouldn't be 0 anymore, instead: $$\nabla \cdot \mathbf{B}= \frac{\rho_{\rm magnetic}}{\mu_0} $$ With $\rho_{\rm magnetic}$ the magnetic charge density, and $\mu_0$ the permeability in vacuum, to interpret it, the divergence of the ...


4

This is a very good question. The same operator algebra does not imply that $H(J,h)$ and $H(h,J)$ have the same spectrum. As has been mentioned in Dominic's answer, even the ground state degeneracy is different under the interchange of $J$ and $h$ ($J\gg h$: symmetry-broken two-fold degeneracy, and $J\ll h$ unique ground state), therefore it is impossible to ...


3

We could say: $$ \frac{\partial \mathbf{B}}{\partial t} \neq 0 \implies \mathbf{\nabla} \times \mathbf{E} \neq 0 \implies \mathbf E \neq 0 $$ Where the first implication follows from the transitivity of inequality and Faraday's law: $$ \mathbf \nabla \times \mathbf E = \frac{\partial \mathbf B }{\partial t } $$ And the second implication is the ...


3

T-duality says that the radius $r$ is equivalent to $\alpha' / r$. So $r+\delta r$ is also equivalent to $\alpha'/(r+\delta r)$, too. If the radius fluctuates, so does its T-dual radius. The radius itself, usefully written as $\sqrt{\alpha'}\exp(\phi_R)$, is a "modulus", a scalar field that has no potential (i.e. all conceivable values are equally allowed: ...


3

Yes, whenever the momentum is conserved and T-duality holds, T-duality must map a conserved quantity such as this momentum to another conserved quantity, i.e. the string winding number in this case, and this fact is independent of the carrier of the momentum or the winding charge. In the general nonperturbative case, you shouldn't think about the charges as ...



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