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We give a non-perturbative proof of a gradient formula for beta functions of two-dimensional quantum field theories. The gradient formula has the form \partial_{i}c = - (g_{ij}+\Delta g_{ij} +b_{ij})\beta^{j} where \beta^{j} are the beta…
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We extensively motivate the studies of higher-derivative gravities, and in particular we emphasize which new quantum features theories with six derivatives in their definitions possess. Next, we discuss the mathematical structure of the…
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Scale invariance profoundly influences the dynamics and structure of complex systems, spanning from critical phenomena to network architecture. Here, we propose a precise definition of scale-invariant networks by leveraging the concept of a…
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The gradient-flow formalism is applied to a non-Abelian gauge theory with scalar and fermionic particles, dubbed "scalar QCD". It is shown that the flowed scalar quark requires a field renormalization, albeit only beyond the one-loop level.…
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One of the main advantages of super-renormalizable higher derivative quantum gravity models is the possibility to derive exact beta functions, by making perturbative one-loop calculations. We perform such a calculation for the Newton…
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