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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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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(∞) field theory, but rather the N→∞ limit of some quantity in SU(N) ...

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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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I would say that $D_\mu '\psi' = U(D_\mu \psi)$ is a requirement, rather than an assumption: When $U$ is a global transformation (i.e., when $\lambda$ is independent of $x$), we have trivially $\partial_\mu \psi' = U(\partial_\mu \psi)$, and so $(\partial_\mu \psi)^\dagger (\partial_\mu \psi) = (\partial_\mu \psi')^\dagger (\partial_\mu \psi')$. We define ...

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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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Here is a partial answer that depends on a particular choice of local gauge constraint. In a U(1) gauge theory, the usual gauge constraint is just Gauss' Law, $$\nabla \cdot \mathbf{E} = \rho.$$ This in turn implies Coulomb's Law $\mathbf{E} \sim 1/r$ for the electric field surrounding a deconfined point charge. Such a long-range interaction ought to be ...

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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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With an answer selected (and bounty awarded) it is time to open a community wiki for explicit references on work along the line of getting QCD + EM, or alternatively QCD alone or QCD + "4th colour" extracting the group from the extra dimensions. An early 1975 work of founding fathers of string theory claims to have a O(6) and then a SU(4) group from the ...

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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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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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While it is certainly possible to get an $SU(3) \times U(1)$ gauge group from the metric alone, if one started with a 9d theory, there are several issues with using Graviphotons as gauge bosons in a 4d theory. Most prominently, in addition to vector bosons you will always create scalars in the adjoint from internal components of the metric, which we do not ...

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OP is considering Yang-Mills theory over a curved base space $(M,g)$. If the base space connection is the Levi-Civita connection $\nabla^{LC}=\partial+\Gamma$, then it doesn't matter whether one uses the gauge-covariant derivative $D=\partial+A$ or the full covariant derivative $\nabla=D+\Gamma$ as the Christoffel symbols $\Gamma$ drops out of the Yang-Mills ...

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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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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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My apologies if I've misestimated where your confusion lies, but what I answer will address some ambiguities that bothers me in some pedagogical expositions. It will also address some common misconceptions. If you are asking what the Hamiltonian is given a parameterized vector potential then it is supposed to be an operator, but the notation about which ...

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