Abstract
We apply the analytic conformal bootstrap method to study weakly coupled conformal gauge theories in four dimensions. We employ twist conformal blocks to find the most general form of the one-loop four-point correlation function of identical scalar operators, without any reference to Feynman calculations. The method relies only on symmetries of the model. In particular, it does not require introducing any regularisation and it is free from the redundancies usually associated with the Feynman approach. By supplementing the general solution with known data for a small number of operators, we recover explicit forms of one-loop correlation functions of four Konishi operators as well as of four half-BPS operators {{mathcal{O}}_{20}}_{prime } in mathcal{N} = 4 super Yang-Mills.
Highlights
In recent years we have substantially advanced our understanding of conformal field theories (CFT) in dimensions higher than two
In this paper we found a family of solutions to the conformal bootstrap equation relevant for the one-loop perturbation of four-dimensional conformal gauge theories
For four-point correlator of scalar operators with dimension ∆ = 2 + g γext + O(g2) we found a fourparameter family of solutions
Summary
In recent years we have substantially advanced our understanding of conformal field theories (CFT) in dimensions higher than two. In order to find a particular four-point correlator we supplement our general solution with a few explicit values of the CFT data for operators with small classical conformal dimension and spin. These can be found in the literature [10,11,12]. We rely on an explicit form of the conformal blocks in four dimensions and the superconformal blocks for the half-BPS operators O20 in N = 4 SYM It was already found in [13, 14] that there exists a class of crossing symmetric solutions which correspond to CFT data that is truncated in spin. We end the paper with conclusions and outlook and supplement it with a few appendices containing the more technical ingredients of our results
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