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Explore the advanced mathematical framework of Yang-Mills theory through this 54-minute conference talk that delves into the five-loop beta function calculations with fermions. Learn about the sophisticated computational techniques required to determine higher-order corrections in quantum field theory, focusing specifically on the renormalization group flow of Yang-Mills gauge theories coupled to fermionic matter. Discover the mathematical challenges involved in multi-loop calculations, the role of dimensional regularization, and the physical significance of beta functions in understanding the running of coupling constants. Examine the technical aspects of Feynman diagram computations at five-loop order, including the treatment of gauge invariance and the systematic approach to handling divergences in quantum field theory. Gain insights into how these calculations contribute to our understanding of asymptotic freedom and the non-Abelian nature of gauge theories, with particular emphasis on the interplay between gauge fields and fermionic degrees of freedom in the quantum corrections.
