scholarly journals Products of current operators in the exact renormalization group formalism

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
H. Sonoda
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Short Distance ◽  
Multiple Products ◽  
Exact Renormalization Group

Abstract Given a Wilson action invariant under global chiral transformations, we can construct current composite operators in terms of the Wilson action. The short-distance singularities in the multiple products of the current operators are taken care of by the exact renormalization group. The Ward–Takahashi identity is compatible with the finite momentum cutoff of the Wilson action. The exact renormalization group and the Ward–Takahashi identity together determine the products. As a concrete example, we study the Gaussian fixed-point Wilson action of the chiral fermions to construct the products of current operators.

scholarly journals The operator algebra at the Gaussian fixed-point

2021 ◽  
pp. 2150106
Author(s):  
H. Sonoda
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Operator Algebra ◽  
Short Distance ◽  
Scaling Properties ◽  
Multiple Products ◽  
Dependent Sources ◽  
Exact Renormalization Group

We consider the multiple products of relevant and marginal scalar composite operators at the Gaussian fixed-point in [Formula: see text] dimensions. This amounts to perturbative construction of the [Formula: see text] theory where the parameters of the theory are momentum-dependent sources. Using the exact renormalization group (ERG) formalism, we show how the scaling properties of the sources are given by the short-distance singularities of the multiple products.

scholarly journals FIELD BEHAVIOR OF AN ISING MODEL WITH APERIODIC INTERACTIONS

2000 ◽  
Vol 14 (14) ◽  
pp. 1473-1480
Author(s):  
ANGSULA GHOSH ◽  
T. A. S. HADDAD ◽  
S. R. SALINAS
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Ising Model ◽  
Critical Behavior ◽  
Nearest Neighbor ◽  
Exchange Interactions ◽  
Universality Class ◽  
Recursion Relations ◽  
Hierarchical Lattices ◽  
Exact Renormalization Group

We derive exact renormalization-group recursion relations for an Ising model, in the presence of external fields, with ferromagnetic nearest-neighbor interactions on Migdal–Kadanoff hierarchical lattices. We consider layered distributions of aperiodic exchange interactions, according to a class of two-letter substitutional sequences. For irrelevant geometric fluctuations, the recursion relations in parameter space display a nontrivial uniform fixed point of hyperbolic character that governs the universal critical behavior. For relevant fluctuations, in agreement with previous work, this fixed point becomes fully unstable, and there appears a two-cycle attractor associated with a new critical universality class.

scholarly journals THE CASE OF ASYMPTOTIC SUPERSYMMETRY

2013 ◽  
Vol 28 (14) ◽  
pp. 1350053 ◽  
Author(s):  
BRUCE L. SÁNCHEZ-VEGA ◽  
ILYA L. SHAPIRO
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Gauge Coupling ◽  
High Energy ◽  
Systematic Investigation ◽  
Coupling Constants ◽  
Scalar Coupling ◽  
Asymptotic State ◽  
Stable Fixed Point ◽  
Scalar Couplings

We start systematic investigation for the possibility to have supersymmetry (SUSY) as an asymptotic state of the gauge theory in the high energy (UV) limit, due to the renormalization group running of coupling constants of the theory. The answer on whether this situation takes place or not, can be resolved by dealing with the running of the ratios between Yukawa and scalar couplings to the gauge coupling. The behavior of these ratios does not depend too much on whether gauge coupling is asymptotically free (AF) or not. It can be shown that the UV stable fixed point for the Yukawa coupling is not supersymmetric. Taking this into account, one can break down SUSY only in the scalar coupling sector. We consider two simplest examples of such breaking, namely N = 1 supersymmetric QED and QCD. In one of the cases one can construct an example of SUSY being restored in the UV regime.

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