
Interpreting RG flows as dynamical systems in the space of couplings we produce a variety of constraints, global (topological) as well as local. These constraints, in turn, rule out some of the proposed RG flows and also predict new phases and fixed points, surprisingly, even in familiar theories such as O(N) model, QED-3, or QCD-4.
62 pp, 25 figures, 6 tables; remarks and references added
High Energy Physics - Theory, Nuclear and High Energy Physics, Strongly Correlated Electrons (cond-mat.str-el), FOS: Physical sciences, QC770-798, Dynamical Systems (math.DS), 530, 620, Condensed Matter - Strongly Correlated Electrons, High Energy Physics - Phenomenology, High Energy Physics - Phenomenology (hep-ph), High Energy Physics - Theory (hep-th), Nuclear and particle physics. Atomic energy. Radioactivity, FOS: Mathematics, Mathematics - Dynamical Systems
High Energy Physics - Theory, Nuclear and High Energy Physics, Strongly Correlated Electrons (cond-mat.str-el), FOS: Physical sciences, QC770-798, Dynamical Systems (math.DS), 530, 620, Condensed Matter - Strongly Correlated Electrons, High Energy Physics - Phenomenology, High Energy Physics - Phenomenology (hep-ph), High Energy Physics - Theory (hep-th), Nuclear and particle physics. Atomic energy. Radioactivity, FOS: Mathematics, Mathematics - Dynamical Systems
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