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Correlation functions of composite operators

Physics Asked on March 13, 2021

I am looking for resources, where there are examples of calculation of correlation functions between composite operators. This is very basic and natural question, but unfortunately, I don’t have any sources..

I am interested in any examples, but if to be concrete, I wanna to understand some basic examples:

  1. $lambda phi^4$ theory:
    $$
    langle phi^2(x) phi^2(y)rangle = ?
    $$

    $$
    langle T_{munu}(x) T_{munu}(y)rangle = ?
    $$

  2. $mathcal{N}=4$ SYM:
    $$
    langle tr(phi_i phi_j) tr(phi_k phi_l) rangle = ?
    $$

One Answer

There is a short section in the book devoted to the correlation functions of composite operators https://www.cambridge.org/core/books/gaugegravity-duality/16CCA2E431B24AEF1B51B0F9C5BE755E. enter image description here

However, as far as I understand, there is not a much information about them, because the renormalization is rather complicated, because instead of simply being multplied by some factor, there arise different operators.

Answered by spiridon_the_sun_rotator on March 13, 2021

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