scholarly journals SU(N) gauge theories in 3+1 dimensions: glueball spectrum, string tensions and topology

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Andreas Athenodorou ◽  
Michael Teper
Keyword(s):  
Topological Charge ◽  
Gauge Theories ◽  
Rotation Group ◽  
String Tension ◽  
Fundamental String ◽  
Running Coupling ◽  
Glueball Spectrum ◽  
Lattice Coupling ◽  
Definition Of ◽  
The Continuum

Abstract We calculate the low-lying glueball spectrum, several string tensions and some properties of topology and the running coupling for SU(N) lattice gauge theories in 3 + 1 dimensions. We do so for 2 ≤ N ≤ 12, using lattice simulations with the Wilson plaquette action, and for glueball states in all the representations of the cubic rotation group, for both values of parity and charge conjugation. We extrapolate these results to the continuum limit of each theory and then to N = ∞. For a number of these states we are able to identify their continuum spins with very little ambiguity. We calculate the fundamental string tension and k = 2 string tension and investigate the N dependence of the ratio. Using the string tension as the scale, we calculate the running of a lattice coupling and confirm that g2(a) ∝ 1/N for constant physics as N → ∞. We fit our calculated values of a√σ with the 3-loop β-function, and extract a value for $$ {\Lambda}_{\overline{MS}} $$ Λ MS ¯ , in units of the string tension, for all our values of N, including SU(3). We use these fits to provide analytic formulae for estimating the string tension at a given lattice coupling. We calculate the topological charge Q for N ≤ 6 where it fluctuates sufficiently for a plausible estimate of the continuum topological susceptibility. We also calculate the renormalisation of the lattice topological charge, ZQ(β), for all our SU(N) gauge theories, using a standard definition of the charge, and we provide interpolating formulae, which may be useful in estimating the renormalisation of the lattice θ parameter. We provide quantitative results for how the topological charge ‘freezes’ with decreasing lattice spacing and with increasing N. Although we are able to show that within our typical errors our glueball and string tension results are insensitive to the freezing of Q at larger N and β, we choose to perform our calculations with a typical distribution of Q imposed upon the fields so as to further reduce any potential systematic errors.

scholarly journals The glueball spectrum of SU(3) gauge theory in 3 + 1 dimensions

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Andreas Athenodorou ◽  
Michael Teper
Keyword(s):  
Gauge Theory ◽  
Continuum Limit ◽  
Lattice Gauge Theory ◽  
Rotation Group ◽  
String Tension ◽  
Energy Scale ◽  
Lattice Gauge ◽  
Glueball Spectrum ◽  
Do So ◽  
The Continuum

Abstract We calculate the low-lying glueball spectrum of the SU(3) lattice gauge theory in 3 + 1 dimensions for the range β ≤ 6.50 using the standard plaquette action. We do so for states in all the representations R of the cubic rotation group, and for both values of parity P and charge conjugation C . We extrapolate these results to the continuum limit of the theory using the confining string tension σ as our energy scale. We also present our results in units of the r0 scale and, from that, in terms of physical ‘GeV’ units. For a number of these states we are able to identify their continuum spins J with very little ambiguity. We also calculate the topological charge Q of the lattice gauge fields so as to show that we have sufficient ergodicity throughout our range of β, and we calculate the multiplicative renormalisation of Q as a function of β. We also obtain the continuum limit of the SU(3) topological susceptibility.

scholarly journals Confinement on R3 × S1: Continuum and lattice

2014 ◽  
Vol 29 (25) ◽  
pp. 1445003
Author(s):  
Michael C. Ogilvie
Keyword(s):  
Gauge Theories ◽  
Lattice Models ◽  
String Tension ◽  
Maximal Abelian Subgroup ◽  
Semiclassical Methods ◽  
Running Coupling ◽  
Substantial Progress ◽  
Abelian Lattice ◽  
Area Law ◽  
The Continuum

There has been substantial progress in understanding confinement in a class of four-dimensional SU(N) gauge theories using semiclassical methods. These models have one or more compact directions, and much of the analysis is based on the physics of finite temperature gauge theories. The topology R3 × S1 has been most often studied using a small compactification circumference L such that the running coupling g2(L) is small. The gauge action is modified by a double-trace Polyakov loop deformation term, or by the addition of periodic adjoint fermions. The additional terms act to preserve Z(N) symmetry and thus confinement. An area law for Wilson loops is induced by a monopole condensate. In the continuum, the string tension can be computed analytically from topological effects. Lattice models display similar behavior, but the theoretical analysis of topological effects is based on Abelian lattice duality rather than on semiclassical arguments. In both cases, the key step is reducing the low-energy symmetry group from SU(N) to the maximal Abelian subgroup U(1)N-1 while maintaining Z(N) symmetry.

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.

TOPOLOGY AND LATTICES

1989 ◽  
Vol 04 (16) ◽  
pp. 1537-1547
Author(s):  
RADEL BEN-AV ◽  
SORIN SOLOMON
Keyword(s):  
Closed Form ◽  
Topological Charge ◽  
Spin Model ◽  
Topological Classification ◽  
Gauge Model ◽  
Homotopy Classes ◽  
Continuous Deformation ◽  
Definition Of ◽  
The Continuum

The concept of interpolation relates lattice configurations to continuum configurations. This relation induces from the continuum to the lattice the definitions of “continuous deformation”, topological classification and homotopy classes. The lattice homotopy classes obtained this way are separated by boundaries made out of “exceptional configurations” (EC). The EC boundaries allow the topological classification of the lattice configurations even in models in which it is impossible (or cumbersome) to give in a closed form, a definition of the topological charge in terms of lattice variables. We give the description of the EC boundaries for the 2-dimensional XY spin model and the 4-dimensional SU(2) gauge model.

scholarly journals Higgs compositeness in Sp(2N) gauge theories — The pure gauge model

2018 ◽  
Vol 175 ◽  
pp. 08013 ◽  
Author(s):  
Ed Bennett ◽  
Deog Ki Hong ◽  
Jong-Wan Lee ◽  
C.-J. David Lin ◽  
Biagio Lucini ◽  
...  
Keyword(s):  
Mass Spectrum ◽  
Lattice Theory ◽  
Gauge Theories ◽  
String Tension ◽  
Numerical Results ◽  
Gauge Model ◽  
Pure Gauge ◽  
Composite Higgs ◽  
Glueball Mass ◽  
The Continuum

As a first step in the study of Sp(2N) composite Higgs models, we obtained a set of novel numerical results for the pure gauge Sp(4) lattice theory in 3+1 space-time dimensions. Results for the continuum extrapolations of the string tension and the glueball mass spectrum are presented and their values are compared with the same quantities in neighbouring SU(N) models.

TORONS, CHIRAL SYMMETRY BREAKING AND U(1) PROBLEM IN QCD AND SQCD

1989 ◽  
Vol 04 (23) ◽  
pp. 2251-2258 ◽  
Author(s):  
A.R. ZHITNITSKY
Keyword(s):  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Crucial Role ◽  
Topological Charge ◽  
Gauge Theories ◽  
Chiral Symmetry Breaking ◽  
Dual Solutions ◽  
New Class ◽  
Manifold With Boundary ◽  
The Continuum

The new class of self-dual solutions with fractional topological charge in SU(2) gauge theories is considered. The solution is defined on manifold with boundary, it has topological charge Q=1/2 and action S=(8π2)/g2×Q. The contribution of the corresponding fluctuations to chiral condensates [Formula: see text], <λ2> in SQCD is calculated and it is consistent with Konishi anomaly. For the fermion condensate in QCD (with Nf=Nc=2, m→0) we find [Formula: see text], [Formula: see text]. The unbound resonances of the continuum at λ=0 play a crucial role in this calculation.

TOPOLOGY AND LATTICES

1990 ◽  
Vol 05 (02) ◽  
pp. 427-437
Author(s):  
RADEL BEN-AV ◽  
SORIN SOLOMON
Keyword(s):  
Topological Charge ◽  
Spin Model ◽  
Topological Classification ◽  
Gauge Model ◽  
Homotopy Classes ◽  
Continuous Deformation ◽  
Definition Of ◽  
Close Form ◽  
The Continuum

The concept of interpolation relates lattice configurations to continuum configurations. This relation induces from the continuum to the lattice the definitions of “continuous deformation”, topological classification and homotopy classes. The lattice homotopy classes obtained this way are separated by boundaries made out of “exceptional configurations” (EC). The EC boundaries allow the topological classification of the lattice configurations even in models in which it is impossible (or cumbersome) to give in a close form, a definition of the topological charge in terms of lattice variables. We give the description of the EC boundaries for the 2 dimensional XY spin model and the 4 dimensional SU(2) gauge model.

scholarly journals Confinement and Pseudoscalar Glueball Spectrum in the 2 + 1D QCD-Like Theory from the Non-Susy D2 Brane

2022 ◽  
Vol 258 ◽  
pp. 10004
Author(s):  
Adrita Chakraborty
Keyword(s):  
Bound States ◽  
String Tension ◽  
Energy Scale ◽  
Coupling Constant ◽  
Running Coupling ◽  
Monotonically Increasing Function ◽  
Glueball Spectrum ◽  
Holographic Approach ◽  
Increasing Function ◽  
Lattice Approach

We study two important properties of 2+1D QCD, namely confinement and Pseudoscalar glueball spectrum, using holographic approach. The confined state of the bounded quark-antiquark pair occurs in the self-coupling dominated nonperturbative regime, where the free gluons form the bound states, known as glueballs. The gauge theory corresponding to low energy decoupled geometry of isotropic non-supersymmetric D2 brane, which is again similar to the 2+1D YM theory, has been taken into account but in this case the coupling constant is found to vary with the energy scale. At BPS limit, this theory reduces to supersymmetric YM theory. We have considered NG action of a test string and calculate the potential of such confined state located on the boundary. The QCD flux tube tension for large quark-antiquark separation is observed to be a monotonically increasing function of running coupling. The mass spectrum of Pseudoscalar glueball is evaluated numerically from the fluctuations of the axion in the gravity theory using WKB approximation. This produces the mass to be related to the string tension and the levels of the first three energy states. The various results that we obtained quite match with those previously studied through the lattice approach.

ГЕРМЕНЕВТИКА ЛИЧНОСТИ КАК МЕТОД СОВРЕМЕННОЙ ПЕРСОНОЛОГИИ

1970 ◽  
Vol 6 (1) ◽  
pp. 32-42
Author(s):  
Елена Старовойтенко
Keyword(s):  
Text Setting ◽  
Research Setting ◽  
Textual Representations ◽  
General Scientific ◽  
Definition Of ◽  
The Individual ◽  
The Continuum

Персонологическая интерпретация текстов предполагает реализацию общенаучных, а также специфических для персонологии, герменевтических установок, к которым относятся: установка на интерпретацию текста как исследование, установка на разнообразие герменевтических действий с текстом, установка на выявление неисследованных содержаний текста, установка на творческое постижение тайн текста, установка на целостное отношение к личности и "Я" автора текста, установка на выявление способности автора быть "практикующим феноменологом", установка на определение места изучаемого текста в континууме текстовых репрезентаций "личности", установка на соотнесение своего понимания текста с другими интерпретациями и их интеграцию, установка на раскрытие сущности авторской "идеи личности", возможное только в единстве интерпретаций, установка на построение и применение герменевтической модели, определяющей процедуру интерпретации как исследования и творчества, установка на определение места проделанного герменевтического поиска в культуре познания и жизни личности, установка на интерпретацию различных видов "текстов личности". Personological interpretation of texts suggests the implementation of the general scientific and also hermeneutical settings specific for Personology which include the setting of the interpretation of the text as a research, setting of a variety of hermeneutical actions with the text, setting to identify unexplored contents of the text, setting of the creative comprehension of the mysteries of the text, setting of the integrity of the attitude of the individual and the "I" of the author of the text, setting to reveal the author's ability to be "practicing phenomenologist", setting of the definition of the place in the text in the continuum of textual representations of the "personality", setting in the correlation of the understanding of the text with other interpretations and their integration, setting of the disclosure of the author's "ideas person" is possible only in the unity of interpretation, setting of the construction and usage of hermeneutical models defining the procedure for the interpretation of both studies and work, the setting to determine the place of hermeneutical research in culture and knowledge of a person's life, setting of the interpretation of various types of "texts of the individual."

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