# Dual Pairs in Four Dimensions

+ 9 like - 0 dislike
270 views

Following the conversation here, I am wondering if anyone knows of an example of dual pair with 4-dimensional N=1 SUSY which relates a non-Abelian gauge theory on one side to a theory with a Lagrangian description but no non-trivial gauge group. Cannot think of one off the top of my head, which doesn't mean it does not exist or even is well-known...

This post has been migrated from (A51.SE)
retagged Apr 19, 2014

+ 9 like - 0 dislike

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 terms of quantum moduli spaces (s-confining when $N_f = N_c + 1$ and chiral symmetry breaking when $N_f = N_c$), with the low energy fields given by mesons and baryons, but you can equally well describe these as the "dual" quarks and mesons of the usual Seiberg duality, in a degenerate limit without gauge fields coupling to them.

Of course, in the same sense, nonsupersymmetric QCD is dual to a theory of massless pions and no gauge symmetry.

This post has been migrated from (A51.SE)
answered Sep 24, 2011 by (1,630 points)
If you mean theories that are dual not just in the sense of having identical IR physics but in the stronger sense of having the same physics along an entire RG flow, then I can't think of an example where one is a gauge theory and the other isn't.

This post has been migrated from (A51.SE)
Yes, I guess duality relevant to that discussion would have to be something stronger than just IR duality. Anyhow, thanks for your answer.

This post has been migrated from (A51.SE)

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysicsOv$\varnothing$rflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.