scholarly journals The four-loop cusp anomalous dimension in $ \mathcal{N} $ = 4 super Yang-Mills and analytic integration techniques for Wilson line integrals

2013 ◽  
Vol 2013 (9) ◽  
Author(s):  
Johannes M. Henn ◽  
Tobias Huber
Keyword(s):  
Anomalous Dimension ◽  
Wilson Line ◽  
Yang Mills ◽  
Analytic Integration ◽  
Integration Techniques ◽  
Cusp Anomalous Dimension

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 structure of IR divergences in celestial gluon amplitudes

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Hernán A. González ◽  
Francisco Rojas
Keyword(s):  
Mellin Transform ◽  
Anomalous Dimension ◽  
Nearest Neighbor ◽  
Wilson Line ◽  
Coulomb Gas ◽  
Vertex Operators ◽  
Positive Quantity ◽  
Colored Scalar ◽  
Cusp Anomalous Dimension ◽  
Hard Function

Abstract The all-loop resummation of SU(N) gauge theory amplitudes is known to factorize into an IR-divergent (soft and collinear) factor and a finite (hard) piece. The divergent factor is universal, whereas the hard function is a process-dependent quantity.We prove that this factorization persists for the corresponding celestial amplitudes. Moreover, the soft/collinear factor becomes a scalar correlator of the product of renormalized Wilson lines defined in terms of celestial data. Their effect on the hard amplitude is a shift in the scaling dimensions by an infinite amount, proportional to the cusp anomalous dimension. This leads us to conclude that the celestial-IR-safe gluon amplitude corresponds to a expectation value of operators dressed with Wilson line primaries. These results hold for finite N.In the large N limit, we show that the soft/collinear correlator can be described in terms of vertex operators in a Coulomb gas of colored scalar primaries with nearest neighbor interactions. In the particular cases of four and five gluons in planar $$ \mathcal{N} $$ N = 4 SYM theory, where the hard factor is known to exponentiate, we establish that the Mellin transform converges in the UV thanks to the fact that the cusp anomalous dimension is a positive quantity. In other words, the very existence of the full celestial amplitude is owed to the positivity of the cusp anomalous dimension.

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 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.

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 Holographic entanglement entropy of the Coulomb branch

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Adam Chalabi ◽  
S. Prem Kumar ◽  
Andy O’Bannon ◽  
Anton Pribytok ◽  
Ronnie Rodgers ◽  
...  
Keyword(s):  
W Boson ◽  
Wilson Line ◽  
Entanglement Entropy ◽  
Physical Principle ◽  
Boson Mass ◽  
Extremal Black Hole ◽  
Energy Tensor ◽  
Large Radius ◽  
Coulomb Branch ◽  
Yang Mills

Abstract We compute entanglement entropy (EE) of a spherical region in (3 + 1)-dimensional $$ \mathcal{N} $$ N = 4 supersymmetric SU(N) Yang-Mills theory in states described holographically by probe D3-branes in AdS5 × S5. We do so by generalising methods for computing EE from a probe brane action without having to determine the probe’s backreaction. On the Coulomb branch with SU(N) broken to SU(N − 1) × U(1), we find the EE monotonically decreases as the sphere’s radius increases, consistent with the a-theorem. The EE of a symmetric-representation Wilson line screened in SU(N − 1) also monotonically decreases, although no known physical principle requires this. A spherical soliton separating SU(N) inside from SU(N − 1) × U(1) outside had been proposed to model an extremal black hole. However, we find the EE of a sphere at the soliton’s radius does not scale with the surface area. For both the screened Wilson line and soliton, the EE at large radius is described by a position-dependent W-boson mass as a short-distance cutoff. Our holographic results for EE and one-point functions of the Lagrangian and stress-energy tensor show that at large distance the soliton looks like a Wilson line in a direct product of fundamental representations.

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