Speaker
Description
Interacting fixed points of the renormalisation group play a central role in determining whether or not quantum field theories exhibit conformal behaviour. In this work, we investigate the conformal windows of weakly coupled fixed points in gauge-matter theories, through a systematic loop-by-loop analysis of perturbative beta functions in the large $N$ Veneziano limit. Our focus is on two complementary settings: the infrared (IR) Banks-Zaks fixed point in asymptotically free gauge theories and the ultraviolet (UV) fixed point of the Litim-Sannino model, which is a gauge-Yukawa theory. For the Banks-Zaks fixed point, we analyse the gauge beta function up to five loop order and study how successive perturbative corrections modify the extent of the IR conformal window. For the Litim-Sannino fixed point, we introduce a projection method that reduces the multi-coupling system to an effective single-coupling beta function, thereby enabling a computationally rigorous investigation of the UV conformal window up to four loop order. For both models, we place a particular emphasis on fixed point mergers as a mechanism that could delimit the conformal window. Our results allow for a comparative assessment of the convergence properties of both models, providing an insight into the reliability and perturbative consistency of their respective conformal windows.