What is the definition of dangerously irrelevant renormalization-group (RG) fixed point?
What are some examples of dangerously irrelevant RG fixed points?
Do we also have the use of dangerously relevant RG fixed points? Do we also have the use of dangerously marginal RG fixed points? What are the examples?
The term "irrelevant, marginal, relevant" are for the IR (infra-red) low energy long distant fixed-point perspective, commonly used in the low energy physics and in condensed matter physics. In high energy and particle physics, people also consider from the UV perspective, thus "irrelevant, marginal, relevant" become "non-renormalizable, renormalizable, super-renormalizable" at the UV (ultra-violet) high energy short distant perspective. So do we also have concepts of: $$ \text{dangerously irrelevant} \leftrightarrow \text{dangerously non-renormalizable}, $$ $$ \text{dangerously marginal} \leftrightarrow \text{dangerously renormalizable}, $$ $$ \text{dangerously relevant} \leftrightarrow \text{dangerously super-renormalizable}, $$
See also a possible example here: Are irrelevant terms in the Kahler potential always irrelevant, even at strong coupling?. Partial answers and partial comments are all welcome. You need not to provide the full answer to write an answer.
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