Timed data flow diagrams

Abstract

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Gauge Invariant Exact Renormalization Group and Perfect Actions in the Open Bosonic String Theory

“…This means the finite cutoff RG equations -or the theory on a lattice with finite spacing -is the same as with a = 0. An action with this property has been described as a "perfect" action [38] -and also earlier similar ideas were introduced under the name of "improved" action [37]. Furthermore if we tune the parameters so that the beta functions are set to zero, then the resulting action is conformally invariant even if a = 0!…”

“…as mentioned in the introducton, there is scale invariance even though the lattice spacing a is non zero. This is the kind of situation envisaged in [37,38] where the coupling constants of the irrelevant operators are all tuned so that the physical quantities calculated with this action do not depend on the cutoff a, and thus they have the same values as in the continuum. These are the "improved" actions [37] or "perfect" actions [38].…”

“…This is the kind of situation envisaged in [37,38] where the coupling constants of the irrelevant operators are all tuned so that the physical quantities calculated with this action do not depend on the cutoff a, and thus they have the same values as in the continuum. These are the "improved" actions [37] or "perfect" actions [38]. If on top of that, the background fields are tuned to satisfy the fixed point condition, then we have a scale invariant theory, even while the lattice spacing is non-zero.…”

“…The phenomenon of scale invariance at finite cutoff is interesting in its own right. This is related to the idea of "improved actions" [37] or "perfect actions" [38] introduced in the context of lattice guage theory. (See also [32,33].)…”

Broken conformal symmetry and hadronic scaling

“…straightforward to see that DK-representations reduce to the symanzik 35) representations for the degenerate series of SU (2,2).…”