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14

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, ...


10

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 ...


9

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

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

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

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

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

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

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

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

"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: ...


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

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 ...


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

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 ...


3

I had seen some such "list" in the papers by Romelsberger and those by Spiridinov and Vartanov. Maybe you are looking for papers like these, Christian Romelsberger, Calculating the Superconformal Index and Seiberg Duality (arXiv:0707.3702) V.P. Spiridonov, G.S. Vartanov, Supersymmetric dualities beyond the conformal window (arXiv:1003.6109)


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 ...


3

It's likely that your mental picture of the "wave" that describes the electron is misleading you. If you're thinking that the electron itself is spread out in the form of the wave and that it's charge is too, then you should rethink your picture. The electron "is" or "behaves like" a wave in that it's state is described by something called a wavefunction. ...


2

Yes. A recent publication looks at the wave-particle duality of large particles (buckminsterfullerene, $\mathrm{C}_{60}$ (actually more of a many-slit experiment)), however the original diffraction experiments with electrons and such were done in the 1920s-1930s and may be hard to access. The authors talk about facile ways to collapse the interference by ...


2

Although in the presence of magnetic monopoles $\mathbf{B}$ can no longer be expressed as the curl of a vector potential, it can still be written as the sum of the curl of a vector potential and the gradient of a scalar potential: $\mathbf{B} = \nabla\Xi + \nabla\times \mathbf{A}$ This is a consequence of Helmholtz's theorem. So, electrodynamics can still ...


2

The duality is inherent in the way we do physics. We never consider the whole universe with all its details. In order to make sense of what we observe (whic his always a small part of the universe only) we - the users of physics - must make a distinction between ''the observed = the system'' and ''the remainder = the environment''. The observed system is ...


2

An answer that Professor Lenny Susskind gave to a non-physicist audience at Stanford in June 2012 went along these lines (by memory and some very short notes I took): The charge on an electron is$\ \alpha \ \approx \ 1/137\ $which means that 99% of the electron is just the bare electron while about 1% of the time it is an electron plus a virtual ...


2

If you mean special conformal transformation x->1/x conformal invariance of Maxwell equations is known since 1909. See here: http://cts.iisc.ernet.in/Personnel/pages/asinha/draft1shouvik.pdf or here: http://arxiv.org/pdf/hep-th/9701064



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