Moose Models (Purpose, Examples)

A problem set for my QFT class is titled "Moose Models" and deals with the moose model for a gauge symmetry of $U(1)\times U(1)$. I was wondering if I could get an explanation of what a Moose Model is, and what it's useful for. Googling things such as "Moose Model Particle Physics" led me to a thesis from Harvard on Minimal Moose Models in $SU(5)$ but it's frankly too advanced for me to do much with. Any help would be appreciated.

-
Besides that Harvard thesis, what other papers have you found? I'm finding a bunch of papers about Moose diagrams. Help us to know where you are with QFT - what is "too advanced" and what are you comfortable with? –  DarenW Mar 15 '13 at 5:12
So my Uni does QFT in three quarters: 1) Scalar Field Theory (From Fock Space to Renormalization Group) 2) QED/SSB: Same idea as in 1st quarter in terms of progress, but now we've covered at least up to the Higgs Mechanism and Gauge Fields 3) Not sure yet, think it's QCD and messing around more with Faddeev-Popov –  MaliciousMalus Mar 15 '13 at 6:01
Maybe this article might help booksc.org/book/13185769 –  nijankowski Mar 15 '13 at 6:25
Thanks for the article, I'll poke through it in the morning and post any questions I have. –  MaliciousMalus Mar 15 '13 at 8:24

1 Answer

If I'm not mistaken, "moose models" are an alternative name for quiver gauge theories. A quiver gauge theory consists of multiple gauge groups, [like $U(1) \times U(1)$ in your example] and "matter" fields charged under multiple gauge groups. For example, quarks in the standard model carry charges under $U(1)_{EM}$, $SU(2)_{Weak}$ and $SU(3)_{Colour}$.. That could be called the "tri-fundamental" representation since the fields are in the fundamental representation of 3 gauge groups. (Whether you would technically call it the "fundamental" rep of EM is debatable but I hope you get the idea.)

These theories are denoted by different kinds of diagrammatic notation. Typically they have blobs representing each gauge group, and edges conecting these blobs represent matter fields (typically in the fundamental rep under both the gauge groups they connect).

If you roughly get what a superconformal (supersymmetric and conformal, as the name says) theory is: This notation seems especially popular in describing superconformal gauge theories. Since the theory is conformal, flow under the renormalization group (RG) (change of energy scale) should not affect coupling constants in the theory. For that to happen, there needs to be a specific constraint on the number of sets (aka flavours) of matter that can sit on each edge -- so that the RG contributions from the gauge fields and matter fields cancel precisely. Since that is understood, diagrams often don't show the matter content and it's implicitly understood from the conformal nature of the theory. These diagrams are known as quiver diagrams or moose diagrams.

I guess the "moose" terminology might be inspired by someone being reminded of moose antlers by looking at these diagrams. You might get more/better results by searching online for "quiver gauge theories"; this name is inspired by mathematical terminology

-
+1. If I recall correctly, calling quivers "moose diagrams" is a Howard Georgi thing. Pity it didn't catch on more widely. –  user1504 Mar 15 '13 at 6:50
Ah! The Georgi connection potentially explains the Harvard thesis on Minimal Moose models in SU(5) :-) –  Siva Mar 15 '13 at 7:16