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if by "gauge transformation in the vielbein" you mean the local lorentz transformation that acts on one of the indices of the vielbein, then the answer is no. Because this local symmetry is in addition to the general coordinate transformation, and not part of it. In other words all veilbeins that are related by a gauged lorentz transformation correspond to ...

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Comments to the question (v4): By definition, the Lagrangian form $\mathbb{L}$ of Chern-Simons (CS) theory (wrt. a Lie algebra valued one-form gauge field $A$) is a CS form, i.e. the CS action reads $$S[A]~=~\int_M\mathbb{L}.$$ The exterior derivative $\mathrm{d}\mathbb{L}$ of a CS form is (also by definition) the Lie algebra trace of a polynomial of the ...

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The rule of the game is to use $A$ and $F=dA$ to write a topological action, and in $d+1$-space time dimension you need to come up with a gauge-invariant $d+1$-form which can then be integrated over the manifold to give you the action. Such an action does not depend on metric at all. Take $U(1)$ gauge field as an example. In $2+1$, the only thing you can ...

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As a beginner for working on relevant topics, I just write few words about your question. I hope it helps you up. Localization Principle has been great role in computing superconformal index also it gives the exact calculation in susy gauge theories. From some excellent works by Pestun, Kapustin, Willet and so on(about a decade ago?), many researcher now ...

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