S-duality in Physics and Fourier Transforms

[mtv65]

In many articles, authors compare S-duality in physics to Fourier transforms.

For example:

Joseph Polchinski, in his article "String Duality" (hep-th/9607050v2), writes "Weak/strong duality [...] is similar to a Fourier transform, where a function which becomes spread out in position space can become very narrow in momentum space. Here though, the Fourier transform is in a complicated nonlinear field space.".

I understand his point, but since the article is from 1996, I wanted to know if someone has, since then, found a more general/precise mathematical definition that would make dualities manifest (paraphrasing Nathan Seiberg - see link below).

Summing up, what I am looking for is:

1. Some procedure to identify if a theory has a S-dual theory.
2. A method to determine this dual theory.

Quoting Nathan Seiberg (www.icts.res.in/sites/default/files/KAWS2018-2018-01-08-Nathan-Seiberg-1.pdf), "we should not be surprised by duality!"

I don't need (nor have any hope of finding) a rigorous mathematical definition. Just something slightly more general and expressed in more mathematical terms would already be fantastic.

 

[LightHero]

Thanks in advance. There is no single procedure or method that can be used to identify and determine S-duality in a theory. However, there are several techniques that can be used to study the phenomenon. One such technique is the Buscher Transformation, which is a set of transformations of the fields and gauge parameters of the theory that map one configuration to another. These transformations can be used to identify dual theories, as they relate the two theories in a precise way.Another technique is the use of conformal field theory, which can be used to study the behavior of a theory under transformation of its fields. In this case, one can study how the theory behaves under S-duality transformations, which will give insight into the dual theory.Finally, the AdS/CFT correspondence is another powerful tool for studying duality. This correspondence allows one to study a conformal field theory in terms of a dual gravitational theory, thus providing insight into the behavior of the theory under S-duality transformations.In summary, while there is no single procedure or method that can definitively identify and determine S-duality in a theory, there are several techniques that can be used to study and better understand the phenomenon.