scholarly journals Gradient flow exact renormalization group

2021 ◽  
Author(s):  
Hidenori Sonoda ◽  
Hiroshi Suzuki
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Lattice Gauge Theory ◽  
Gradient Flow ◽  
Continuum Theory ◽  
Coarse Graining ◽  
Yang Mills ◽  
Guiding Principle ◽  
Lattice Gauge ◽  
Exact Renormalization Group

Abstract The gradient flow bears a close resemblance to the coarse graining, the guiding principle of the renormalization group (RG). In the case of scalar field theory, a precise connection has been made between the gradient flow and the RG flow of the Wilson action in the exact renormalization group (ERG) formalism. By imitating the structure of this connection, we propose an ERG differential equation that preserves manifest gauge invariance in Yang{Mills theory. Our construction in continuum theory can be extended to lattice gauge theory.

COMPACTIFICATION OF SPACE-TIME DIMENSIONS IN LATTICE GAUGE THEORY

1988 ◽  
Vol 03 (06) ◽  
pp. 1423-1434 ◽  
Author(s):  
C.B. LANG ◽  
M. PILCH ◽  
B.-S. SKAGERSTAM
Keyword(s):  
Gauge Theory ◽  
Lattice Gauge Theory ◽  
Continuum Theory ◽  
Scalar Fields ◽  
Effective Theory ◽  
Tree Level ◽  
Yang Mills ◽  
Lattice Gauge ◽  
First Order Phase Transition ◽  
First Order Phase

The pure SU(2) Yang-Mills gauge field theory is studied in D=5 Euclidean dimensions in which case the continuum theory is nonrenormalizable. By a compactification of one dimension the effective theory, on the tree level, is equivalent to a D=4 SU(2) gauge theory with adjoint scalar fields. In a Monte Carlo (MC) simulation of the lattice regularized theory we confirm the existence of a first order phase transition; on asymmetric lattices we also find a higher order phase “finite temperature” transition. It is argued that the low energy continuum limit of the compactified theory nonperturbatively agrees with the renormalizable adjoint Higgs model in D=4 in the unbroken, confining phase.

APPLICATION OF EXACT RENORMALIZATION GROUP TECHNIQUES TO THE NON-PERTURBATIVE STUDY OF SUPERSYMMETRIC FIELD THEORY

2004 ◽  
Vol 18 (04n05) ◽  
pp. 469-478 ◽  
Author(s):  
STEFANO ARNONE ◽  
KENSUKE YOSHIDA
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Renormalization Group Equation ◽  
Group Method ◽  
Group Equation ◽  
Renormalization Group Method ◽  
Exact Relation ◽  
Yang Mills ◽  
Supersymmetric Gauge ◽  
Exact Renormalization Group

A simple form of the exact renormalization group method is proposed for the study of supersymmetric gauge field theory. The method relies on the existence of ultraviolet-finite four dimensional gauge theories with extended supersymmetry. The resulting exact renormalization group equation crucially depends on the Konishi anomaly of N=1 super Yang–Mills. We illustrate our method by dealing with the NSVZ exact relation for the beta functions, the N=2 super Yang–Mills effective potential and the N=1 super Yang–Mills gluon superpotential (the so-called Veneziano–Yankielowicz potential).

scholarly journals GAUGE INVARIANT EXACT RENORMALIZATION GROUP AND PERFECT ACTIONS IN THE OPEN BOSONIC STRING THEORY

2007 ◽  
Vol 22 (23) ◽  
pp. 1701-1715 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Renormalization Group ◽  
Lattice Gauge Theory ◽  
Equations Of Motion ◽  
Finite Lattice ◽  
Open String ◽  
Scale Invariant ◽  
Gauge Invariant ◽  
Lattice Gauge ◽  
Exact Renormalization Group ◽  
The Continuum

The exact renormalization group is applied to the worldsheet theory describing bosonic open string backgrounds to obtain the equations of motion for the fields of the open string. Using loop variable techniques the equations can be constructed to be gauge invariant. Furthermore they are valid off the (free) mass shell. This requires keeping a finite cutoff. Thus we have the interesting situation of a scale invariant worldsheet theory with a finite worldsheet cutoff. This is possible because there is infinite number of operators whose coefficients can be tuned. This is in the same sense that "perfect actions" or "improved actions" have been proposed in lattice gauge theory to reproduce the continuum results even while keeping a finite lattice spacing.

scholarly journals A MANIFESTLY GAUGE INVARIANT AND UNIVERSAL CALCULUS FORSU(N) YANG–MILLS

2006 ◽  
Vol 21 (23n24) ◽  
pp. 4627-4761 ◽  
Author(s):  
OLIVER J. ROSTEN
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Explicit Dependence ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Group A ◽  
Β Function ◽  
Exact Renormalization Group

Within the framework of the Exact Renormalization Group, a manifestly gauge invariant calculus is constructed for SU (N) Yang–Mills. The methodology is comprehensively illustrated with a proof, to all orders in perturbation theory, that the β function has no explicit dependence on either the seed action or details of the covariantization of the cutoff. The cancellation of these nonuniversal contributions is done in an entirely diagrammatic fashion.

Stability of renormalization group fixed points and decay of correlations

2019 ◽  
pp. 101-110
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Fixed Points ◽  
Gradient Flow ◽  
Scalar Fields ◽  
Effective Field ◽  
Coupling Constants ◽  
Critical Systems ◽  
Universal Properties ◽  
General Physical

Chapter 7 is devoted to a discussion of the renormalization group (RG) flow when the effective field theory that describes universal properties of critical phenomena depends on several coupling constants. The universal properties of a large class of macroscopic phase transitions with short range interactions can be described by statistical field theories involving scalar fields with quartic interactions. The simplest critical systems have an O(N) orthogonal symmetry and, therefore, the corresponding field theory has only one quartic interaction. However, in more general physical systems, the flow of quartic interactions is more complicated. This chapter examines these systems from the RG viewpoint. RG beta functions are shown to generate a gradient flow. Some examples illustrate the notion of emergent symmetry. The local stability of fixed points is related to the value of the scaling field dimension.

SU (N) lattice-gauge theory in the Migdal renormalization group model

1991 ◽  
Vol 264 (3-4) ◽  
pp. 401-406 ◽  
Author(s):  
N. Tanimura ◽  
W. Scheid ◽  
O. Tanimura
Keyword(s):  
Renormalization Group ◽  
Gauge Theory ◽  
Lattice Gauge Theory ◽  
Group Model ◽  
Lattice Gauge

scholarly journals THE EXACT RENORMALIZATION GROUP IN ASTROPHYSICS

2001 ◽  
Vol 16 (11) ◽  
pp. 2041-2046 ◽  
Author(s):  
JOSÉ GAITE
Keyword(s):  
Renormalization Group ◽  
Probability Distribution ◽  
Time Evolution ◽  
Planck Equation ◽  
Coarse Graining ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Change Of Scale ◽  
Exact Renormalization Group ◽  
Fokker Planck

The coarse-graining operation in hydrodynamics is equivalent to a change of scale which can be formalized as a renormalization group transformation. In particular, its application to the probability distribution of a self-gravitating fluid yields an "exact renormalization group equation" of Fokker-Planck type. Since the time evolution of that distribution can also be described by a Fokker-Planck equation, we propose a connection between both equations, that is, a connection between scale and time evolution. We finally remark on the essentially non-perturbative nature of astrophysical problems, which suggests that the exact renormalization group is the adequate tool for them.

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