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The following was meant to be a comment rather than an answer. However, since it was a bit long for a comment so I am writing it in the answer box. In the case of a field theory, states can be thought of as functions on the space of boundary conditions on a spatial slice. This is so because the space of boundary conditions on a spatial slice is the ...

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Inserting a local operator means multiplying the integrand of the path integral by an operator with fixed position. This way, only the value of the operator at this position contributes to the path integral. If you now assume that the operator is an insertion at the position $z=0$, which in the present context of radial quantization corresponds to the ...

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I've got the answer by myself. Simply do Taylor expansion of the left hand side. Expand both the exponential, and the field around $H(0)$ or $\psi(0)$, then the right hand follows naturally after plugging in definitions of $T_B$.

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AdS/CFT correspondence tells you (among other things) the dual geometry for each state of the boundary theory. As @Arnold says (check the link in the comment), a finite temperature state ("spontaneously") breaks Lorentz, and hence, conformal invariance. That's okay because excited states could break many symmetries of the theory (eg: p-shell of electron ...

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Firstly, I'd like to recommend Conformal Field Theory by Di-Francesco, it is a comprehensive text which is thorough and contains many applications of conformal field theory. The text is indispensable. In conformal field theory, it is often characteristic of correlation functions to diverge as points of two or more fields coincide. The operator product ...

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