Recent results on renormalization-group evolution of theories with gauge, fermion, and scalar fields

2017 ◽  
Vol 32 (35) ◽  
pp. 1747007
Author(s):  
R. Shrock
Keyword(s):  
Renormalization Group ◽  
Gauge Theory ◽  
Anomalous Dimension ◽  
Beta Function ◽  
Scalar Fields ◽  
Group Behavior ◽  
Abelian Gauge ◽  
Dimension Formula ◽  
Technicolor Model ◽  
Group Evolution

We discuss recent results on renormalization-group evolution of several types of theories. First, we consider asymptotically free vectorial gauge theories with various fermion contents and discuss higher-loop calculations of the UV to IR evolution in these theories, including an IR zero of the beta function and the value of the anomalous dimension [Formula: see text] at this point, together with comparisons with lattice measurements. Effects of scheme transformations are discussed. We then present a novel way to determine the value of [Formula: see text] in an [Formula: see text] technicolor model from a particular embedding in an extended technicolor theory. Finally, we analyze the renormalization-group behavior of several non-asymptotically free theories, including a U(1) gauge theory, a non-Abelian gauge theory with many fermions, an [Formula: see text] [Formula: see text] scalar theory, and Yukawa theories.

scholarly journals THE BV MASTER EQUATION FOR THE WILSON ACTION IN GENERAL YANG-MILLS GAUGE THEORY

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2255-2256
Author(s):  
TAKESHI HIGASHI ◽  
ETSUKO ITOU ◽  
TAICHIRO KUGO
Keyword(s):  
Renormalization Group ◽  
Gauge Theory ◽  
Master Equation ◽  
Effective Action ◽  
Gauge Invariance ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Yang Mills ◽  
Usual Form

We study the four dimensional gauge theory within Wilsonian Renormalization Group (WRG) method. The Wilson effective action for general Yang-Mills gauge theory is shown to satisfy the usual form of Batalin-Vilkovisky (BV) master equation, despite that a momentum cutoff apparently breaks the gauge invariance. In the case of Abelian gauge theory, in particular, it actually deduces the Ward-Takahashi identity for Wilson action recently derived by Sonoda. We elucidated the relation of our Wilson master action with that derived by Ref. 2 and, in particular, showed that our BV Master equation really reproduced the Sonoda's WT identity for the Wilson action in QED. (This is a proceeding to the conference based on the poster given by E.I.).

scholarly journals MAXWELL SYMMETRIES AND SOME APPLICATIONS

2013 ◽  
Vol 23 ◽  
pp. 350-356 ◽  
Author(s):  
JOSÉ A. DE AZCÁRRAGA ◽  
KIYOSHI KAMIMURA ◽  
JERZY LUKIERSKI
Keyword(s):  
Gauge Theory ◽  
Gravity Field ◽  
Scalar Fields ◽  
Cosmological Term ◽  
Gauge Fields ◽  
Spin Connection ◽  
Field Equations ◽  
Geometric Framework ◽  
Abelian Gauge ◽  
Poincaré Algebra

The Maxwell algebra is the result of enlarging the Poincaré algebra by six additional tensorial Abelian generators that make the fourmomenta non-commutative. We present a local gauge theory based on the Maxwell algebra with vierbein, spin connection and six additional geometric Abelian gauge fields. We apply this geometric framework to the construction of Maxwell gravity, which is described by the Einstein action plus a generalized cosmological term. We mention a Friedman-Robertson-Walker cosmological approximation to the Maxwell gravity field equations, with two scalar fields obtained from the additional gauge fields. Finally, we outline further developments of the Maxwell symmetries framework.

scholarly journals Renormalizable Abelian-Projected Effective Gauge Theory Derived from Quantum Chromodynamics II

2003 ◽  
Vol 18 (20) ◽  
pp. 1403-1412 ◽  
Author(s):  
Toru Shinohara
Keyword(s):  
Gauge Theory ◽  
Tensor Field ◽  
Anomalous Dimension ◽  
Low Energy ◽  
Effective Theory ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Antisymmetric Tensor Field ◽  
Group Functions ◽  
Multiplicative Renormalizability

In the previous paper,1 we derived the Abelian projected effective gauge theory as a low energy effective theory of the SU (N) Yang–Mills theory by adopting the maximal Abelian gauge. At that time, we have demonstrated the multiplicative renormalizability of the propagators for the diagonal gluon and the dual Abelian antisymmetric tensor field. In this paper, we show the multiplicative renormalizability of the Green's functions also for the off-diagonal gluon. Moreover, we complement the previous results by calculating the anomalous dimension and the renormalization group functions which are undetermined in the previous paper.

scholarly journals UPPER BOUND ON THE MASS SCALE OF SUPERPARTNERS IN MINIMAL N = 2 SUPERSYMMETRY

2007 ◽  
Vol 22 (33) ◽  
pp. 2539-2547 ◽  
Author(s):  
BISWAJOY BRAHMACHARI
Keyword(s):  
Renormalization Group ◽  
Gauge Theory ◽  
Upper Bound ◽  
Threshold Effect ◽  
Mass Scale ◽  
Low Energy ◽  
Intermediate Scale ◽  
Central Value ◽  
Renormalization Group Equations ◽  
Group Evolution

If N = 2 supersymmetry breaks to N = 1 supersymmetry at an intermediate scale m2 and then, later on, N = 1 supersymmetry breaks and produces standard model at a scale m susy such that m2>m susy , renormalization group evolution of three gauge couplings are altered above the scale m2, changing the unification scale and the unified coupling. We show that when we enforce this general condition m2>m susy on the solutions of the renormalization group equations, the condition is translated into an upper bound on the scale m susy . Using presently favored values of α1(mz), α2(mz), α3(mz), we get m susy < 4.5 ×109 GeV for the central value of α3(mZ). When low energy threshold effect is present, this bound gets smeared yet remains generally stable in the 109–1010 GeV range. We also show that if we demand string unification instead of having a unified gauge theory, this constraint can be changed by exotic hypercharge normalizations.

scholarly journals BRST in the exact renormalization group

2019 ◽  
Vol 2019 (10) ◽  
Author(s):  
Yuji Igarashi ◽  
Katsumi Itoh ◽  
Tim R Morris
Keyword(s):  
Renormalization Group ◽  
Effective Action ◽  
Beta Function ◽  
Mass Term ◽  
Flow Equation ◽  
Tree Level ◽  
Quantum Master Equation ◽  
Abelian Gauge ◽  
Brst Invariance ◽  
Slavnov Taylor Identities

Abstract We show, explicitly within perturbation theory, that the quantum master equation and the Wilsonian renormalization group flow equation can be combined such that for the continuum effective action, quantum BRST invariance is not broken by the presence of an effective ultraviolet cutoff $\Lambda$, despite the fact that the structure demands quantum corrections that naïvely break the gauge invariance, such as a mass term for a non-Abelian gauge field. Exploiting the derivative expansion, BRST cohomological methods fix the solution up to choice of renormalization conditions, without inputting the form of the classical, or bare, interactions. Legendre transformation results in an equivalent description in terms of solving the modified Slavnov–Taylor identities and the flow of the Legendre effective action under an infrared cutoff $\Lambda$ (i.e. effective average action). The flow generates a canonical transformation that automatically solves the Slavnov–Taylor identities for the wavefunction renormalization constants. We confirm this structure in detail at tree level and one loop. Under flow of $\Lambda$, the standard results are obtained for the beta function, anomalous dimension, and physical amplitudes, up to the choice of the renormalization scheme.

scholarly journals GAUGE CONSISTENT WILSON RENORMALIZATION GROUP II: THE NON-ABELIAN CASE

2000 ◽  
Vol 15 (14) ◽  
pp. 2153-2179 ◽  
Author(s):  
M. SIMIONATO
Keyword(s):  
Renormalization Group ◽  
Gauge Theories ◽  
Beta Function ◽  
Ward Identities ◽  
Abelian Gauge ◽  
Axial Gauge ◽  
Abelian Case ◽  
Group Ii ◽  
The One ◽  
Wilson Renormalization Group

We give a Wilsonian formulation of non-Abelian gauge theories explicitly consistent with axial gauge Ward identities. The issues of unitarity and dependence on the quantization direction are carefully investigated. A Wilsonian computation of the one-loop QCD beta function is performed.

scholarly journals Cwebs beyond three loops in multiparton amplitudes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Neelima Agarwal ◽  
Lorenzo Magnea ◽  
Sourav Pal ◽  
Anurag Tripathi
Keyword(s):  
Gauge Theories ◽  
Anomalous Dimension ◽  
Wilson Line ◽  
Building Blocks ◽  
Feynman Diagrams ◽  
Loop Order ◽  
Abelian Gauge ◽  
Sum Rule ◽  
Combinatorial Properties ◽  
Low Dimensional

Abstract Correlators of Wilson-line operators in non-abelian gauge theories are known to exponentiate, and their logarithms can be organised in terms of collections of Feynman diagrams called webs. In [1] we introduced the concept of Cweb, or correlator web, which is a set of skeleton diagrams built with connected gluon correlators, and we computed the mixing matrices for all Cwebs connecting four or five Wilson lines at four loops. Here we complete the evaluation of four-loop mixing matrices, presenting the results for all Cwebs connecting two and three Wilson lines. We observe that the conjuctured column sum rule is obeyed by all the mixing matrices that appear at four-loops. We also show how low-dimensional mixing matrices can be uniquely determined from their known combinatorial properties, and provide some all-order results for selected classes of mixing matrices. Our results complete the required colour building blocks for the calculation of the soft anomalous dimension matrix at four-loop order.

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