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3

There are apparently several thousand references to "SU(\infty)" on arxiv.org, and some of them are definitely talking about gauge fields or Yang-Mills. I suspect that some of the time, this will just be a way of talking about the large N limit of SU(N), i.e., not referring to a literal SU(āˆž) field theory, but rather the Nā†’āˆž limit of some quantity in SU(N) ...


2

Comments to the question (v2): The idea to consider the planar large $N_c\to \infty$ limit in $SU(N_c)$ QCD goes back to Ref. 1. In light-cone membrane theory, pioneered in Ref. 2, the group $SU(\infty)$ is naturally identified with area-preserving diffeomorphisms ${\rm SDiff}_0(T^2)$ on the torus $T^2$ connected to the identity. Concretely, OP's proposal ...


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Here is a very "quick and dirty" way to get the result, too long for a comment so I'll post it as an answer: Although condensation is essentially a quantum phenomena, for many purposes it is sufficient to think at the classical level, e.g. Meissner effect. The Maxwell electrodynamics with both electric and magnetic charges famously has a $S$-duality ...


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First, terminology: You are not "determining the gauge group", what you are doing in gauge fixing is determining a smooth choice of (hopefully only) one representant of an equivalence class of field configurations called the gauge orbit. Geometrically, you are seeking a section which intersects each gauge orbit exactly once. The problem of finding a gauge ...


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Let the equations of motion be expressed in a frame with coordinates $q$. We now want to switch over to another (arbitrarily moving) frame, whose corresponding coordinates are $Q$, given by: $$Q = f(q, t)$$ For example, if the frame itself is moving with position $x(t)$, we will have: $$Q = q - x(t)$$ (where $x$ is not dynamic, but is completely specified in ...


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You have a few different questions here, so let's try to go through them one by one. When we make the chiral symmetry local, have we introduced a gauge symmetry, or some analogue of a gauge symmetry? When you make the chiral symmetry local you introduce a gauge symmetry. The terms "gauge symmetry" and "local symmetry" are two different ways of saying the ...


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Is the existence of deconfined gauge charges a sufficient condition to ensure gaplessness? I think the answer is NO, such as the $Z_2$ gauge theory in 2+1D and 3+1D. I believe that the existence of deconfined gauge charges of a continuous gauge group is a sufficient condition to ensure gaplessness? Hastings and I have a paper ...


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The scalar potential of your theory is $$V(\phi) = \lambda (\phi^a \phi^a - v^2)^2,$$ where I suspect you meant to take the square as I've written here. This potential is minimized when $\sqrt{\phi^a \phi^a} = v$. Think of $\phi=\frac{1}{2} \phi^a \sigma^a$ as a vector with components $\phi^a$ in a 3-dimensional vector space with basis vectors $\sigma_a/2$. ...


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The Berry connection lives in the parameter space, thus it appears not in the microscopic Hamiltonian given in the question but in the effective Hamiltonian equation of motion in the parameter space. The aim, in the following, is to show the details in the variational approximation. To be precise, the bra-ket notation that I'll be using is explained in ...



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