scholarly journals Boomerang webs up to three-loop order

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Einan Gardi ◽  
Mark Harley ◽  
Rebecca Lodin ◽  
Martina Palusa ◽  
Jennifer M. Smillie ◽  
...  
Keyword(s):  
Gauge Theory ◽  
Anomalous Dimension ◽  
Wilson Line ◽  
Feynman Diagrams ◽  
Loop Order ◽  
Colour Factor ◽  
Gluon Exchange ◽  
Self Energy ◽  
Replica Trick ◽  
The Web

Abstract Webs are sets of Feynman diagrams which manifest soft gluon exponentiation in gauge theory scattering amplitudes: individual webs contribute to the logarithm of the amplitude and their ultraviolet renormalization encodes its infrared structure. In this paper, we consider the particular class of boomerang webs, consisting of multiple gluon exchanges, but where at least one gluon has both of its endpoints on the same Wilson line. First, we use the replica trick to prove that diagrams involving self-energy insertions along the Wilson line do not contribute to the web, i.e. their exponentiated colour factor vanishes. Consequently boomerang webs effectively involve only integrals where boomerang gluons straddle one or more gluons that connect to other Wilson lines. Next we classify and calculate all boomerang webs involving semi-infinite non-lightlike Wilson lines up to three-loop order, including a detailed discussion of how to regulate and renormalize them. Furthermore, we show that they can be written using a basis of specific harmonic polylogarithms, that has been conjectured to be sufficient for expressing all multiple gluon exchange webs. However, boomerang webs differ from other gluon-exchange webs by featuring a lower and non-uniform transcendental weight. We cross-check our results by showing how certain boomerang webs can be determined by the so-called collinear reduction of previously calculated webs. Our results are a necessary ingredient of the soft anomalous dimension for non-lightlike Wilson lines at three loops.

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 Boundary electromagnetic duality from homological edge modes

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Philippe Mathieu ◽  
Nicholas Teh
Keyword(s):  
Gauge Theory ◽  
Symplectic Structure ◽  
Central Charge ◽  
Wilson Line ◽  
Boundary Term ◽  
Global Symmetry ◽  
Homotopy Pullback ◽  
Line Singularities ◽  
Topological Boundary

Abstract Recent years have seen a renewed interest in using ‘edge modes’ to extend the pre-symplectic structure of gauge theory on manifolds with boundaries. Here we further the investigation undertaken in [1] by using the formalism of homotopy pullback and Deligne- Beilinson cohomology to describe an electromagnetic (EM) duality on the boundary of M = B3 × ℝ. Upon breaking a generalized global symmetry, the duality is implemented by a BF-like topological boundary term. We then introduce Wilson line singularities on ∂M and show that these induce the existence of dual edge modes, which we identify as connections over a (−1)-gerbe. We derive the pre-symplectic structure that yields the central charge in [1] and show that the central charge is related to a non-trivial class of the (−1)-gerbe.

scholarly journals One-loop matching for spin-dependent quasi-TMDs

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Markus A. Ebert ◽  
Stella T. Schindler ◽  
Iain W. Stewart ◽  
Yong Zhao
Keyword(s):  
Spin Structure ◽  
Wilson Line ◽  
Three Dimensional ◽  
Distribution Functions ◽  
Longitudinal Momentum ◽  
Loop Order ◽  
Parton Distribution Functions ◽  
Transverse Momentum Dependent ◽  
Unique Probe ◽  
Transverse Position

Abstract Transverse momentum dependent parton distribution functions (TMDPDFs) provide a unique probe of the three-dimensional spin structure of hadrons. We construct spin-dependent quasi-TMDPDFs that are amenable to lattice QCD calculations and that can be used to determine spin-dependent TMDPDFs. We calculate the short-distance coefficients connecting spin-dependent TMDPDFs and quasi-TMDPDFs at one-loop order. We find that the helicity and transversity distributions have the same coefficient as the unpolarized TMDPDF. We also argue that the same is true for pretzelosity and that this spin universality of the matching will hold to all orders in αs. Thus, it is possible to calculate ratios of these distributions as a function of longitudinal momentum and transverse position utilizing simpler Wilson line paths than have previously been considered.

scholarly journals DISCRETE NONCOMMUTATIVE GAUGE THEORY

2001 ◽  
Vol 16 (04n06) ◽  
pp. 367-386 ◽  
Author(s):  
RICHARD J. SZABO
Keyword(s):  
Gauge Theory ◽  
Matrix Models ◽  
Wilson Line ◽  
Morita Equivalence ◽  
Generic Properties ◽  
Gauge Invariant ◽  
Fundamental Matter ◽  
Generic Relation ◽  
Noncommutative Gauge Theory ◽  
Noncommutative Quantum

A review of the relationships between matrix models and noncommutative gauge theory is presented. A lattice version of noncommutative Yang–Mills theory is constructed and used to examine some generic properties of noncommutative quantum field theory, such as uv/ir mixing and the appearance of gauge-invariant open Wilson line operators. Morita equivalence in this class of models is derived and used to establish the generic relation between noncommutative gauge theory and twisted reduced models. Finite-dimensional representations of the quotient conditions for toroidal compactification of matrix models are thereby exhibited. The coupling of noncommutative gauge fields to fundamental matter fields is considered and a large mass expansion is used to study the properties of gauge-invariant observables. Morita equivalence with fundamental matter is also presented and used to prove the equivalence between the planar loop renormalizations in commutative and noncommutative quantum chromodynamics.

scholarly journals Directed Percolation: Calculation of Feynman Diagrams in the Three-Loop Approximation

2018 ◽  
Vol 173 ◽  
pp. 02001 ◽  
Author(s):  
Loran Ts. Adzhemyan ◽  
Michal Hnatič ◽  
Mikhail V. Kompaniets ◽  
Tomáš Lučivjanský ◽  
Lukáš Mižišin
Keyword(s):  
Perturbation Theory ◽  
Statistical Physics ◽  
Numerical Technique ◽  
Feynman Diagrams ◽  
Directed Percolation ◽  
Loop Order ◽  
Percolation Process ◽  
Anomalous Dimensions ◽  
Loop Approximation ◽  
Universal Properties

The directed bond percolation process is an important model in statistical physics. By now its universal properties are known only up to the second-order of the perturbation theory. Here, our aim is to put forward a numerical technique with anomalous dimensions of directed percolation to higher orders of perturbation theory and is focused on the most complicated Feynman diagrams with problems in calculation. The anomalous dimensions are computed up to three-loop order in ε = 4 − d.

scholarly journals A Feynman integral via higher normal functions

2015 ◽  
Vol 151 (12) ◽  
pp. 2329-2375 ◽  
Author(s):  
Spencer Bloch ◽  
Matt Kerr ◽  
Pierre Vanhove
Keyword(s):  
Critical Value ◽  
Feynman Integral ◽  
The Other ◽  
Roots Of Unity ◽  
Critical Strip ◽  
Loop Order ◽  
Motivic Cohomology ◽  
Self Energy ◽  
Normal Functions ◽  
Inhomogeneous Solution

We study the Feynman integral for the three-banana graph defined as the scalar two-point self-energy at three-loop order. The Feynman integral is evaluated for all identical internal masses in two space-time dimensions. Two calculations are given for the Feynman integral: one based on an interpretation of the integral as an inhomogeneous solution of a classical Picard–Fuchs differential equation, and the other using arithmetic algebraic geometry, motivic cohomology, and Eisenstein series. Both methods use the rather special fact that the Feynman integral is a family of regulator periods associated to a family of$K3$surfaces. We show that the integral is given by a sum of elliptic trilogarithms evaluated at sixth roots of unity. This elliptic trilogarithm value is related to the regulator of a class in the motivic cohomology of the$K3$family. We prove a conjecture by David Broadhurst which states that at a special kinematical point the Feynman integral is given by a critical value of the Hasse–Weil$L$-function of the$K3$surface. This result is shown to be a particular case of Deligne’s conjectures relating values of$L$-functions inside the critical strip to periods.

scholarly journals ON THE β-FUNCTION AND CONFORMAL ANOMALY OF NONCOMMUTATIVE QED WITH ADJOINT MATTER FIELDS

2003 ◽  
Vol 18 (15) ◽  
pp. 2591-2607 ◽  
Author(s):  
NÉDA SADOOGHI ◽  
MOJTABA MOHAMMADI
Keyword(s):  
Gauge Theory ◽  
Integral Method ◽  
Degrees Of Freedom ◽  
Adjoint Representation ◽  
Conformal Anomaly ◽  
Loop Order ◽  
Path Integral Method ◽  
Β Function ◽  
The One ◽  
Matter Fields

In the first part of this work, a perturbative analysis up to one-loop order is carried out to determine the one-loop β-function of noncommutative U(1) gauge theory with matter fields in the adjoint representation. In the second part, the conformal anomaly of the same theory is calculated using Fujikawa's path integral method. The value of the one-loop β-function calculated in both methods coincides. As it turns out, noncommutative QED with matter fields in the adjoint representation is asymptotically free for the number of flavor degrees of freedom Nf < 3.

scholarly journals On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order

2007 ◽  
Vol 322 (10) ◽  
pp. 2374-2445 ◽  
Author(s):  
S. Groote ◽  
J.G. Körner ◽  
A.A. Pivovarov
Keyword(s):  
Feynman Diagrams ◽  
Loop Order

scholarly journals Operator regularization of Feynman diagrams at multiloop order

2011 ◽  
Vol 89 (11) ◽  
pp. 1149-1154 ◽  
Author(s):  
A.Y. Shiekh
Keyword(s):  
Zeta Function ◽  
Dimensional Regularization ◽  
Feynman Diagrams ◽  
Loop Order

It has been previously believed not possible to use operator regularization with Feynman diagrams, but such an option would greatly simplify matters, as operator regularization is otherwise limited to the more complicated Schwinger approach. Further, operator regularization, unlike zeta function regularization, is not limited to one-loop order, and preserves supersymmetry, unlike dimensional regularization. In this work, we investigate operator regularization at the more probing two-loop order, and find not only compatibility but that the simplification associated with Feynman diagrams is retained.

scholarly journals Spin Structure Functions of the Nucleon and Twist-3 Operators in QCD

1997 ◽  
Vol 50 (1) ◽  
pp. 79 ◽  
Author(s):  
Kazuhiro Tanaka
Keyword(s):  
Spin Structure ◽  
Unique Feature ◽  
Anomalous Dimension ◽  
Equations Of Motion ◽  
Distribution Functions ◽  
View Point ◽  
Loop Order ◽  
Parton Distribution Functions ◽  
Parton Distributions ◽  
The One

We investigate the twist-3 spin-dependent parton distribution functions hL(x; Q2) and gT (x; Q2). We discuss the physical relevance of the parton distributions from the view point of the factorization theorem in QCD. A unique feature of the ‘measurable’ higher-twist distributions hL and gT is emphasized. We investigate the Q2 -evolution of hL and gT in the framework of the renormalization group and standard QCD perturbation theory. We calculate the anomalous dimension matrix for the twist-3 operators for hL and gT in the one-loop order. The operator mixing among the relevant twist-3 operators, including the operators proportional to the QCD equations of motion, is treated properly in a consistent scheme. Implications for future experiments are also discussed.

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