2025/09/08 by Singh, Swapnil kumar
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Cosmology and Gravitation Theories
paper · pdf · doi:10.48550/arxiv.2509.06799
We study the three-loop gauge β-functions in general N=1 supersymmetric gauge theories regularized by higher covariant derivatives (HCD) supplemented with Pauli--Villars subtraction. The all-structure three-loop form of the β-functions in the HCD framework is known and involves regulator-dependent parameters. Here we evaluate these parameters explicitly for the exponential regulators R(x)=exn and F(x)=exm. We obtain the constants A(n) and B(m) in closed form, together with their large-n,m asymptotics, and substitute them into the general three-loop expressions. This yields fully explicit, regulator-parameterized β-functions and a systematic expansion in 1/n and 1/m that organizes finite, scheme-dependent terms. We then exhibit finite coupling redefinitions that map the renormalized DR result to a scheme compatible with the Novikov--Shifman--Vainshtein--Zakharov relation. Our analysis clarifies how exponential higher-derivative regulators preserve this relation at the bare level and illustrates the regulator-driven structure of supersymmetric renormalization group flows.