scholarly journals Generalised cusp anomalous dimension in β−deformed super Yang Mills theory

2013 ◽  
Vol 2013 (10) ◽  
Author(s):  
George Georgiou ◽  
Dimitrios Giataganas
Keyword(s):  
Anomalous Dimension ◽  
Yang Mills ◽  
Cusp Anomalous Dimension ◽  
Super Yang Mills Theory

scholarly journals The full four-loop cusp anomalous dimension in N$$ \mathcal{N} $$ = 4 super Yang-Mills and QCD

2020 ◽  
Vol 2020 (4) ◽  
Author(s):  
Johannes M. Henn ◽  
Gregory P. Korchemsky ◽  
Bernhard Mistlberger
Keyword(s):  
Anomalous Dimension ◽  
Yang Mills ◽  
Cusp Anomalous Dimension

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 Four-loop planar amplitude and cusp anomalous dimension in maximally supersymmetric Yang-Mills theory

2007 ◽  
Vol 75 (8) ◽  
Author(s):  
Zvi Bern ◽  
Michael Czakon ◽  
Lance J. Dixon ◽  
David A. Kosower ◽  
Vladimir A. Smirnov
Keyword(s):  
Anomalous Dimension ◽  
Yang Mills ◽  
Cusp Anomalous Dimension

scholarly journals Super Yang-Mills theories with inhomogeneous mass deformations

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yoonbai Kim ◽  
O-Kab Kwon ◽  
D. D. Tolla
Keyword(s):  
Boundary Condition ◽  
Killing Spinor ◽  
Vacuum Equation ◽  
Constant Mass ◽  
Yang Mills ◽  
Spatial Coordinate ◽  
Mass Functions ◽  
Vacuum Solutions ◽  
Super Yang Mills Theory

Abstract We construct the 4-dimensional $$ \mathcal{N}=\frac{1}{2} $$ N = 1 2 and $$ \mathcal{N} $$ N = 1 inhomogeneously mass-deformed super Yang-Mills theories from the $$ \mathcal{N} $$ N = 1* and $$ \mathcal{N} $$ N = 2* theories, respectively, and analyse their supersymmetric vacua. The inhomogeneity is attributed to the dependence of background fluxes in the type IIB supergravity on a single spatial coordinate. This gives rise to inhomogeneous mass functions in the $$ \mathcal{N} $$ N = 4 super Yang-Mills theory which describes the dynamics of D3-branes. The Killing spinor equations for those inhomogeneous theories lead to the supersymmetric vacuum equation and a boundary condition. We investigate two types of solutions in the $$ \mathcal{N}=\frac{1}{2} $$ N = 1 2 theory, corresponding to the cases of asymptotically constant mass functions and periodic mass functions. For the former case, the boundary condition gives a relation between the parameters of two possibly distinct vacua at the asymptotic boundaries. Brane interpretations for corresponding vacuum solutions in type IIB supergravity are also discussed. For the latter case, we obtain explicit forms of the periodic vacuum solutions.

scholarly journals Exact 1/N expansion of Wilson loop correlators in $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Wolfgang Mück
Keyword(s):  
Matrix Model ◽  
Wilson Loop ◽  
Model Solution ◽  
Wilson Loops ◽  
Combinatorial Formula ◽  
Expectation Value ◽  
Yang Mills ◽  
Hooft Coupling ◽  
The Matrix ◽  
Super Yang Mills Theory

Abstract Supersymmetric circular Wilson loops in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills theory are discussed starting from their Gaussian matrix model representations. Previous results on the generating functions of Wilson loops are reviewed and extended to the more general case of two different loop contours, which is needed to discuss coincident loops with opposite orientations. A combinatorial formula representing the connected correlators of multiply wound Wilson loops in terms of the matrix model solution is derived. Two new results are obtained on the expectation value of the circular Wilson loop, the expansion of which into a series in 1/N and to all orders in the ’t Hooft coupling λ was derived by Drukker and Gross about twenty years ago. The connected correlators of two multiply wound Wilson loops with arbitrary winding numbers are calculated as a series in 1/N. The coefficient functions are derived not only as power series in λ, but also to all orders in λ by expressing them in terms of the coefficients of the Drukker and Gross series. This provides an efficient way to calculate the 1/N series, which can probably be generalized to higher-point correlators.

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.

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