scholarly journals RI/MOM renormalization of the parton quasidistribution functions in lattice regularization

2021 ◽  
Vol 104 (7) ◽  
Author(s):  
Kuan Zhang ◽  
Yuan-Yuan Li ◽  
Yi-Kai Huo ◽  
Andreas Schäfer ◽  
Peng Sun ◽  
...  
Keyword(s):  
Lattice Regularization

scholarly journals Eigenvalue spectrum and scaling dimension of lattice $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Georg Bergner ◽  
David Schaich
Keyword(s):  
Anomalous Dimension ◽  
Finite Lattice ◽  
Continuum Theory ◽  
Lattice Volume ◽  
Yang Mills ◽  
Lattice Regularization ◽  
Perturbative Renormalization ◽  
Zero Values ◽  
Definition Of ◽  
Group Flow

Abstract We investigate the lattice regularization of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory, by stochastically computing the eigenvalue mode number of the fermion operator. This provides important insight into the non-perturbative renormalization group flow of the lattice theory, through the definition of a scale-dependent effective mass anomalous dimension. While this anomalous dimension is expected to vanish in the conformal continuum theory, the finite lattice volume and lattice spacing generically lead to non-zero values, which we use to study the approach to the continuum limit. Our numerical results, comparing multiple lattice volumes, ’t Hooft couplings, and numbers of colors, confirm convergence towards the expected continuum result, while quantifying the increasing significance of lattice artifacts at larger couplings.

scholarly journals 4D N = 1 SYM supercurrent on the lattice in terms of the gradient flow

2018 ◽  
Vol 175 ◽  
pp. 11014
Author(s):  
Kenji Hieda ◽  
Aya Kasai ◽  
Hiroki Makino ◽  
Hiroshi Suzuki
Keyword(s):  
Gradient Flow ◽  
Independent Manner ◽  
Yang Mills ◽  
Loop Level ◽  
Lattice Regularization ◽  
The One ◽  
Noether Current ◽  
Super Yang Mills Theory

The gradient flow [1–5] gives rise to a versatile method to construct renor-malized composite operators in a regularization-independent manner. By adopting this method, the authors of Refs. [6–9] obtained the expression of Noether currents on the lattice in the cases where the associated symmetries are broken by lattice regularization. We apply the same method to the Noether current associated with supersymmetry, i.e., the supercurrent. We consider the 4D N = 1 super Yang–Mills theory and calculate the renormalized supercurrent in the one-loop level in the Wess–Zumino gauge. We then re-express this supercurrent in terms of the flowed gauge and flowed gaugino fields [10].

scholarly journals Hadron physics from lattice QCD

2016 ◽  
Vol 25 (07) ◽  
pp. 1642008 ◽  
Author(s):  
Wolfgang Bietenholz
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Quantum Field ◽  
Chiral Perturbation ◽  
Hadron Physics ◽  
Lattice Regularization ◽  
Sign Problem ◽  
Hadron Masses ◽  
Basic Ideas

We sketch the basic ideas of the lattice regularization in Quantum Field Theory, the corresponding Monte Carlo simulations, and applications to Quantum Chromodynamics (QCD). This approach enables the numerical measurement of observables at the non-perturbative level. We comment on selected results, with a focus on hadron masses and the link to Chiral Perturbation Theory. At last, we address two outstanding issues: topological freezing and the sign problem.

scholarly journals LATTICE GAUGE THEORIES AND THE AdS/CFT CORRESPONDENCE

2000 ◽  
Vol 15 (25) ◽  
pp. 3901-3966 ◽  
Author(s):  
M. CASELLE
Keyword(s):  
Gauge Theories ◽  
String Tension ◽  
Yang Mills ◽  
Lattice Gauge ◽  
Lattice Regularization ◽  
Glueball Spectrum ◽  
Lattice Gauge Theories ◽  
Basic Features

This review is devoted to a comparison between lattice gauge theories and AdS/CFT results for the nonperturbative behavior of nonsupersymmetric Yang–Mills theories. It is intended for readers who are assumed not to be experts in LGT. For this reason the first part is devoted to a pedagogical introduction to the Lattice regularization of QCD. In the second part we discuss some basic features of the AdS/CFT correspondence and compare the results obtained in the nonsupersymmetric limit with those obtained on the lattice. We discuss in particular the behavior of the string tension and of the glueball spectrum.

Quantum anomalies: A few physics applications

2019 ◽  
pp. 283-318
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Particle Physics ◽  
Anomaly Cancellation ◽  
Quantum Theories ◽  
Axial Anomaly ◽  
Gauge Symmetries ◽  
Classical Symmetries ◽  
Lattice Regularization ◽  
The Standard Model ◽  
Quantum Anomalies ◽  
Definition Of

Chapter 17 exhibits various examples where classical symmetries cannot be transferred to quantum theories. The obstructions are characterized by anomalies. The examples involve chiral symmetries combined with currents or gauge symmetries, leading to chiral anomalies. In particular, anomalies lead to obstruction in the construction of theories. In particular, the structure of the Standard Model of particle physics is constrained by the requirement of anomaly cancellation. Other applications, like the relation between electromagnetic pi0 decay and the axial anomaly, are described. Anomalies are related to the Dirac operator index, leading to relations between anomaly and topology. To prove anomaly cancellation beyond perturbation theory, one can use lattice regularization. However, the definition of lattice chiral transformations is non–trivial. It is based on solutions of the Ginsparg–Wilson relation.

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