| Abstract |
This thesis is occupied with the collective methods known in the literature as the analytic bootstrap. The analytic bootstrap is one of the many existing techniques, which study conformal field theories (CFTs). It relies heavily on conformal invariance and the use of the crossing equation to reproduce universal results for generic CFTs and properties of particular models. Our first concern is to reproduce the theoretical foundation of a generic CFT, which will constitute the base of our upcoming analysis. We start our review on the analytic bootstrap by introducing the inversion formula, a relation analytic in spin, which connects the relevant physical information of a CFT with the double-discontinuities appearing on the four-point function. We also present the systematics of large spin perturbation theory (LSPT), which involve the more convenient expressions of twist conformal blocks (TCBs) and a relative frame for working on interacting CFTs in a perturbative setting. The combination of the inversion formula and LSPT provides us with the necessary formalism, so as to study the famous Wilson-Fischer model in d = 4 − ε dimensions and reproduce the means for obtaining several known results up to fourth-order in the expansion parameter. Among them lie the OPE coefficients and the anomalous dimensions of the intermediate operators appearing in the spectrum, the corrections of the external operator φ up to second order in the expansion parameter and the central charge of the theory up to fourth order in the expansion parameter. The last result is considered to be especially significant as it can be extracted with a relative ease compared to the other methods used for the same purpose.
purpose.
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Conformal field theories and analytic Bootstrap
