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Let $\overline{\mathbb{R}^{p,q}}$ denote the conformal compactification of $\mathbb{R}^{p,q}$. Let $n:=p+q$. [If $n=1$, then any transformation is automatically a conformal transformation, so let's assume $n\geq 2$.] On one hand, there is the (global) conformal group consisting of the set globally defined conformal transformations on ...

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I found the mistake. (1) The state $(L_{-2}^{(1)} + L_{-2}^{(2)})|0\rangle$ does correspond to the total stress tensor for the product CFT. Acting on this state with the lowering operator $L_{2}^{(1)} + L_{2}^{(2)}$ gives a state proportional to the vacuum (except in the case where the central charge $c=0-$then the stress tensor is primary. (2) The state ...

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I happen upon this old thread now. Maybe it is still worth giving an update, and more of an answer. The latest account (as of the time of this writing) of the conjectural statement in question here appears as Conjecture 1.17 in Stephan Stolz, Peter Teichner, Supersymmetric field theories and generalized cohomology in H. Sati, U. Schreiber (eds.) ...

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Unfortunately, Bardeen seems to misunderstand the naturalness problem that has nothing to do with quadratic divergences per se. In the strict SM, there is no naturalness problem because the running Higgs mass squared is proportional to itself. But this is not the setup that people care about when talking about the actual naturalness problem that emerges ...

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The physical limit is $a\to 0$ so the terms in the operator that are subleading in $a/L$ go to zero and may be neglected. This is a different situation from computing various sums and integrals (in Green's functions and scattering amplitudes) whose leading terms in an expansion diverge. The leading divergent piece may be unphysical and get subtracted by ...

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