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Are there simple analogues of AdS/CFT duality that are understandable without any knowledge of string theory?
Haelfix said:There are many types of dualities. The simplest ones that are often taught to students is the Massless Sine-Gordon and Massive Thirring model duality.
Also the Montonen–Olive duality between Electric and magnetic charges.
Perhaps you wanted something more sophisticated?
A. Neumaier said:I'd like to have something that helps me to get a good idea of what is going on in AdS/CFT duality without having to work with the latter directly.
A. Neumaier said:So that working with the simpler model helps me to tackle later the real thing.
I am interested in AdS/CFT not because of unification (which I think is a still elusive far away goal) but because it can successfully be used to model hadrons, e.g., http://arxiv.org/pdf/0802.0514 , and hence be compared with experiment.Fra said:I'v understood from your other posts that you are working on some axiomatisations and formalisations of QM: But from which perspective is AdS/CFT the "real thing"? That sounds strange to me.
As I understand it, AdS/CFT as in the AdS5 × S5 / N=4 YM is merely a specific example of an implementation of some version of the holographic principle. But to me the "real thing" would be to arrive at some in depth, general understanding of what the physical holographic principle really is, and why. This is not not existing. The reason AdS/CFT becomes to discussed is because it's as far as I know one of the few detailed examples.
Thanks, I'll look into that.Haelfix said:Yea, this doesn't really exist. The closest that I know off would be the derivation of Brown and Henneaux in 2+1 dimensional gravity which is in some sense a precursor of AdS/CFT. It has the advantage that you don't need to know string theory, and motivates the holographic principle. Historically it was more of an odd calculation that struck people as interesting, but it wasn't necessarily appreciated that a duality could be hiding there. This does serve as a decent warmup though!
Brown, J. D.; Henneaux, M. (1986). "Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity". Communications in Mathematical Physics 104 (2): 207–226
Ynaught? said:Have you considered the way in which a holographic image emerges from a hologram? This is an article in "plain English" by Juan Maldacena discussing AdS/CFT correspondence and the Holographic Principle. http://www.sns.ias.edu/~malda/sciam-maldacena-3a.pdf
A. Neumaier said:Or is duality just a name for different descriptions of equivalent theories? If that, I am somewhat surprised -- I had expected something justifying the label ''duality''. What was the reason for choosing this word?
A. Neumaier said:Are there simple analogues of AdS/CFT duality that are understandable without any knowledge of string theory?
Maybe to the insider, but for me it is just the right level of explanation.Physics Monkey said:I think it's fair to say that duality often refers to two descriptions of the same physical system. There is an informal requirement that these descriptions be "sufficiently different" and address "complementary" aspects of the physical system.
Let me give a few examples (I apologize in advance as I'm sure much of this well known):
Physics Monkey said:In addition to my last long post, I would also point out that one doesn't really need string theory to understand AdS/CFT.
All the basic computations can be carried out with limited reference to string theory. I give a few examples below for the dictionary at large N. [...]
Of course, this is only the tip of the iceberg.
A. Neumaier said:But I thought string theory is supposed to live in 10 or 11 dimensions. So how do these
items connect?
JollyJoker said:Does anyone know a simple case where an extra dimension emerges? I'm thinking about something like how sound is basically just air pressure over time, with frequency giving you a third dimension that is convenient in some cases and adds odd properties like an uncertainty principle.
JollyJoker said:Does anyone know a simple case where an extra dimension emerges? I'm thinking about something like how sound is basically just air pressure over time, with frequency giving you a third dimension that is convenient in some cases and adds odd properties like an uncertainty principle.
mitchell porter said:I think it would be conceptually helpful to also study (1) http://www.staff.science.uu.nl/~hooft101/gthpub/planar_diagram_theory.pdf"
The 1/N expansion is a way of organizing the Feynman diagrams, according to the genus of the minimal surface capable of containing them. The planar limit is where you only consider planar diagrams. But the other diagrams exist and correspond to multiloop amplitudes in the string theory (loops in the string theory = handles on the string worldsheet = genus of the worldsheet-CFT Riemann surface = genus of the summed diagrams in the gauge theory).A. Neumaier said:Isn't the 1/N limit a classical theory? So where is the dual quantum theory?
Duality in science refers to the concept that certain phenomena or theories can be described or understood in two different ways, often seemingly contradictory. It can also refer to the idea that two seemingly separate entities or concepts are actually interconnected and dependent on each other.
Duality is significant in scientific research because it allows for a deeper understanding and broader perspective on a particular phenomenon or theory. It also encourages scientists to think critically and consider multiple viewpoints, leading to more comprehensive and accurate conclusions.
Duality applies to various fields of science, such as physics, mathematics, biology, and psychology. In physics, duality is often observed in the wave-particle duality of light and matter. In mathematics, it is seen in the duality principle, where certain concepts can be described in two different ways. In biology, duality is evident in the complementary roles of DNA and RNA in genetics. In psychology, it can be seen in the interplay between nature and nurture in human development.
Yes, duality can be observed in everyday life. For example, the concept of light and darkness, or good and evil, can be seen as dualities. In music, the harmony between different notes and the contrast between major and minor chords also demonstrate duality. Additionally, the concept of mind and body in philosophy can be seen as a duality.
Duality plays a significant role in shaping scientific theories and models. It allows for a more comprehensive and holistic understanding of complex phenomena, leading to the development of more accurate and robust theories. Duality can also challenge existing theories and lead to new discoveries and breakthroughs in scientific research.