Seiberg Duality (or dualities)

[arivero]

Lads, what is your understanding of Seiberg duality? I am using as source the book of Terning, that seems pretty decent, and somehow I don't seem to catch the basic intuitions about what maps to what and why.

It can be a old trauma... first time I heard Witten was in Paris about 1993 presenting Seiberg-Witten and he did a so pretty talk that it seemed trivial to me, and then everyone telling that that was going to produce hundreds of papers.

 

[mitchell porter]

There are some recommendations here

https://imaginarypotential.wordpress.com/2008/03/19/susy-qcdseiberg-duality-reading-list/

I used to rely on the start of Strassler for the basics.

Seiberg-Witten theory is a whole different thing! Seiberg duality is to a large extent about anomaly matching (a la 't Hooft) in the context of N=1 SUSY. Seiberg-Witten theory is about confinement in N=2 SUSY and has immediate connections to string duality (e.g. with the "Seiberg-Witten curve" having a direct geometric interpretation as the shape of two compact extra dimensions).

While we're on the topic, let me give my version of the Eric Weinstein controversy associated with Seiberg-Witten theory.

As mentioned, Seiberg-Witten theory describes confinement in N=2 super-Yang-Mills - in terms of an N=1 super-Yang-Mills effective theory.

Witten also used Seiberg-Witten to radically simplify Donaldson theory, which characterizes 4-manifolds using SU(2) gauge theory. Witten took a "topologically twisted" form of N=2 SU(2) gauge theory, applied the Seiberg-Witten ansatz, and ended up with a non-susy theory consisting of a bosonic spinor coupled to a U(1) gauge theory, as an EFT for N=2 Donaldson theory.

Eric Weinstein has received a lot of scorn for claiming that he came up with this "Donaldson-Witten theory" himself, at an earlier date, while exploring his own theory of everything. But in fact it makes sense that Donaldson-Witten theory has a gravitational interpretation, since it descends from SU(2) gauge theory, and the Ashtekar variables turn gravity into a kind of SU(2) gauge theory. That's a connection-based theory of gravity (rather than metric-based), and Weinstein's theory is a connection-based theory of everything, and I suspect he had an idea something like that Donaldson-Witten EFT, but perhaps missing some technical nuance.

 

[arivero]

the old website has a lost link, fortunately on archive https://web.archive.org/web/20141014035926/http://www.physics.uc.edu/~argyres/661/susy1996.pdf

I think weinstein should has been more active in internet forums and that would help his memory. I can not accurately remember 2005 anymore, except thanks to PF!