# Tag Info

15

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, ...

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, ...

7

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 ...

7

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 ...

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, ...

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

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 ...

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 ...

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 ...

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

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 ...

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

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 ...

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)

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

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

2

The reason is that string theory is a proper S-matrix theory--- it defines things by probing at infinity using probes in the theory, and classical things using the massless fields at infinity as classical probes. The D-brane carries a mass density and a charge density, and when it is classical, the two are related as for an extremal black hole. This relation ...

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 ...

1

In other words, wasn't Young wrong and Newton right, instead of them both being right? Localization defines what most physicists would think of as particles ie. yes, Newton's aether - ridding nature of its inert stage. But 20th century physics still hinges on the inert stage and cannot deny that waves are at the heart of the SM. But if we can modify the ...

1

String field theory can't deal with the modular invariance. Indeed, that's a reason that there is no known consistent string field theory which contains and describes external physical closed string states. This is a paradoxical proposition from me because the first string theory paper in my life that I studied in detail, one about the Kyoto group string ...

1

You correctly noticed that in some interpretations there is a "split" between "quantum" and "classical" and this split is somewhat arbitrary. You can move it closer to the observer without loosing consistency. If you make it to the extreme and move it as close to the observer as possible you will find that the whole universe follows certain laws such as ...

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To take a different approach to the variety of ways in which you present QM (which all seem fine, but perhaps they miss the underlying structure), we compute expected values of an observable $O$ using the trace rule in QM, $E[O]=\mathsf{Tr}[\hat O\hat\rho]$, in which on one side there is an operator that represents a measurement and on the other side there ...

1

You need to know the basic Fourier transform delta-function identity $$\int_{-\infty}^{\infty} e^{ikx} {dk\over 2\pi} = \delta(x)$$ Which implies Fourier inversion. Proving this identity is slightly subtle, because the right hand side is a distribution, but you can do the integral explicitly over a long interval from -M to M to get an object which has a ...

1

If you want a paper that explicitly shows the loss of interference due to a "which slit" measurement, the following work by Dave Pritchard's group at MIT (using sodium atoms) is one very nice example. Journal reference: Physical Review Letters vol. 75 pg. 3783 Nov 1995 Free to read: http://cua.mit.edu/Pritchard_IFM/Publications/photon_scattering.pdf ...

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