Renormdynamics and production of fractals, fluctons, solitons, strings, unparticles, …

Abstract

Abstract. Concise introduction in renormdynamics with solvable models of (non)perturbative QCD and exotic states of fractals, fluctons, solitons, strings, unparticles...We say that we find New Physics (NP) when either we find a phenomenon which is forbidden by SM in principle -this is the qualitative level of NP -or we find a significant deviation between precision calculations in SM of an observable quantity and a corresponding experimental value.In QFT existence of a given theory means, that we can control its behavior at some scales (short or large distances) by renormalization theory [3]. If the theory exists, then we want to solve it, which means to determine what happens on other (large or short) scales. This is the problem (and content) of Renormdynamics. The result of the Renormdynamics, the solution of its discrete or continuous motion equations, is the effective QFT on a given scale (different from the initial one).We will call Renormdynamics Functions (RDF) functions g n = f n (t) which are solutions of the RD motion equationsġIn the simplest case of one coupling constant the function g = f (t) is constant, g = g c when β(g c ) = 0, or is invertible (monotone). Indeed,ġEach monotone interval ends by UV and IR fixed points and describes corresponding phase of the system. Note that the simplest case of the classical dynamics, the Hamiltonian system with one degree of freedom, is already two-dimensional, so we have no analog of one charge renormdynamics. In the string theory, the connection between conformal invariance of the effective theory on the parametric world sheet and the motion equations of the fields on the embedding space is well known [8]. A more recent topic in this direction is AdS/CFT Duality [10]. In this approach for QCD coupling constant the following expression was obtained [2] α AdS (Q 2 ) = α(0)e −Q 2 /4k 2 .A corresponding β-function is β(α AdS ) = dα AdS d ln Q 2 = − Q 2 4k 2 α AdS (Q 2 ) = α AdS (Q 2 ) ln α AdS (Q 2 ) α(0) ≤ 0 (4)