scholarly journals Loop equation and exact soft anomalous dimension in $$ \mathcal{N} $$ = 4 super Yang-Mills

2020 ◽  
Vol 2020 (6) ◽  
Author(s):  
Simone Giombi ◽  
Shota Komatsu
Keyword(s):  
Anomalous Dimension ◽  
Yang Mills ◽  
Loop Equation

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 The High Spin Expansion of Twist Sector Dimensions: The Planar𝒩=4Super Yang-Mills Theory

2010 ◽  
Vol 2010 ◽  
pp. 1-30 ◽  
Author(s):  
Davide Fioravanti ◽  
Marco Rossi
Keyword(s):  
High Spin ◽  
Gauge Theories ◽  
Anomalous Dimension ◽  
Yang Mills ◽  
Analysis Tools ◽  
Twist Operators ◽  
Super Yang Mills Theory

This review is devoted to collecting some results on the high spin expansion of (minimal) anomalous dimension. Thanks to the recent rationale on integrability, planar𝒩=4super Yang-Mills theory (or itsAdS5×S5string counterpart) represents a very practicable field. Here the attention will be restricted to its sector of twist operators, although the analysis tools are quite general (in integrable theories). Some structures and ideas turn out to be general also for other sectors or gauge theories.

scholarly journals CONSTRAINTS ON CONFORMAL WINDOWS FROM HOLOGRAPHIC DUALS

2011 ◽  
Vol 26 (30) ◽  
pp. 2227-2246 ◽  
Author(s):  
O. ANTIPIN ◽  
K. TUOMINEN
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Functional Form ◽  
Anomalous Dimension ◽  
Beta Function ◽  
Analytic Form ◽  
Yang Mills ◽  
Conformal Window ◽  
Holographic Duals ◽  
Dimensional Gravity

We analyze a beta function with the analytic form of Novikov–Shifman–Vainshtein–Zakharov result in the five-dimensional gravity-dilaton environment. We show how dilaton inherits poles and fixed points of such beta function through the zeros and points of extremum in its potential. Super Yang–Mills and supersymmetric QCD are studied in detail and Seiberg's electric-magnetic duality in the dilaton potential is explicitly demonstrated. Non-supersymmetric proposals of similar functional form are tested and new insights into the conformal window as well as determinations of scheme-independent value of the anomalous dimension at the fixed point are presented.

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 Three-loop universal anomalous dimension of the Wilson operators in N=4 SUSY Yang–Mills model

2004 ◽  
Vol 595 (1-4) ◽  
pp. 521-529 ◽  
Author(s):  
A.V. Kotikov ◽  
L.N. Lipatov ◽  
A.I. Onishchenko ◽  
V.N. Velizhanin
Keyword(s):  
Anomalous Dimension ◽  
Yang Mills

scholarly journals QUANTUM STRINGS IN AdS5 × S5 AND GAUGE–STRING DUALITY

2010 ◽  
Vol 25 (02n03) ◽  
pp. 319-331 ◽  
Author(s):  
A. A. TSEYTLIN
Keyword(s):  
String Duality ◽  
Strong Coupling ◽  
Recent Progress ◽  
Anomalous Dimension ◽  
General Structure ◽  
Strong Coupling Expansion ◽  
Massive String ◽  
Yang Mills ◽  
Extract Information

We review some recent progress in understanding the spectrum of energies/dimensions of strings/operators in AdS5 × S5 – planar [Formula: see text] super Yang-Mills correspondence. We consider leading strong coupling corrections to the energy of lightest massive string modes in AdS5 × S5, which should be dual to members of the Konishi operator multiplet in the SYM theory. This determines the general structure of strong-coupling expansion of the anomalous dimension of the Konishi operator. We use 1-loop results for semiclassical string states to extract information about the leading coefficients in this expansion.

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