scholarly journals Wilson Loops in the Adjoint Representation and Multiple Vacua in Two-Dimensional Yang–Mills Theory

2000 ◽  
Vol 285 (2) ◽  
pp. 185-220 ◽  
Author(s):  
A. Bassetto ◽  
L. Griguolo ◽  
F. Vian
Keyword(s):  
Adjoint Representation ◽  
Wilson Loops ◽  
Two Dimensional ◽  
Yang Mills

scholarly journals Large-N behavior of the Wilson loops of generalized two-dimensional Yang–Mills theories

2006 ◽  
Vol 733 (1-2) ◽  
pp. 123-131 ◽  
Author(s):  
M. Khorrami ◽  
M. Alimohammadi
Keyword(s):  
Wilson Loops ◽  
Two Dimensional ◽  
Yang Mills ◽  
Large N

scholarly journals Double-winding Wilson loops in SU(N) Yang-Mills theory – A criterion for testing the confinement models –

2018 ◽  
Vol 175 ◽  
pp. 12002
Author(s):  
Ryutaro Matsudo ◽  
Kei-Ichi Kondo ◽  
Akihiro Shibata
Keyword(s):  
Wilson Loop ◽  
String Tension ◽  
Wilson Loops ◽  
Two Dimensional ◽  
Fundamental Representation ◽  
Yang Mills ◽  
Operator Relation ◽  
Higher Dimensional ◽  
The Difference ◽  
Area Law

We examine how the average of double-winding Wilson loops depends on the number of color N in the SU(N) Yang-Mills theory. In the case where the two loops C1 and C2 are identical, we derive the exact operator relation which relates the doublewinding Wilson loop operator in the fundamental representation to that in the higher dimensional representations depending on N. By taking the average of the relation, we find that the difference-of-areas law for the area law falloff recently claimed for N = 2 is excluded for N ⩾ 3, provided that the string tension obeys the Casimir scaling for the higher representations. In the case where the two loops are distinct, we argue that the area law follows a novel law (N − 3)A1/(N − 1) + A2 with A1 and A2(A1 < A2) being the minimal areas spanned respectively by the loops C1 and C2, which is neither sum-ofareas (A1 + A2) nor difference-of-areas (A2 − A1) law when (N ⩾ 3). Indeed, this behavior can be confirmed in the two-dimensional SU(N) Yang-Mills theory exactly.

scholarly journals Calculation of Wilson Loops in Two-Dimensional Yang–Mills Theories

2000 ◽  
Vol 283 (1) ◽  
pp. 11-56 ◽  
Author(s):  
J.M. Aroca ◽  
Yu. Kubyshin
Keyword(s):  
Wilson Loops ◽  
Two Dimensional ◽  
Yang Mills

scholarly journals Bootstrapping octagons in reduced kinematics from A2 cluster algebras

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Song He ◽  
Zhenjie Li ◽  
Yichao Tang ◽  
Qinglin Yang
Keyword(s):  
Scattering Amplitudes ◽  
Minkowski Spacetime ◽  
Dimensional Subspace ◽  
Cluster Algebras ◽  
Wilson Loops ◽  
Two Dimensional ◽  
Feynman Integrals ◽  
Yang Mills ◽  
Two Sectors ◽  
Special Case

Abstract Multi-loop scattering amplitudes/null polygonal Wilson loops in $$ \mathcal{N} $$ N = 4 super-Yang-Mills are known to simplify significantly in reduced kinematics, where external legs/edges lie in an 1 + 1 dimensional subspace of Minkowski spacetime (or boundary of the AdS3 subspace). Since the edges of a 2n-gon with even and odd labels go along two different null directions, the kinematics is reduced to two copies of G(2, n)/T ∼ An−3. In the simplest octagon case, we conjecture that all loop amplitudes and Feynman integrals are given in terms of two overlapping A2 functions (a special case of two-dimensional harmonic polylogarithms): in addition to the letters v, 1 + v, w, 1 + w of A1 × A1, there are two letters v − w, 1 − vw mixing the two sectors but they never appear together in the same term; these are the reduced version of four-mass-box algebraic letters. Evidence supporting our conjecture includes all known octagon amplitudes as well as new computations of multi-loop integrals in reduced kinematics. By leveraging this alphabet and conditions on first and last entries, we initiate a bootstrap program in reduced kinematics: within the remarkably simple space of overlapping A2 functions, we easily obtain octagon amplitudes up to two-loop NMHV and three-loop MHV. We also briefly comment on the generalization to 2n-gons in terms of A2 functions and beyond.

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 On topological recursion for Wilson loops in $$ \mathcal{N} $$ = 4 SYM at strong coupling

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
M. Beccaria ◽  
A. Hasan
Keyword(s):  
Strong Coupling ◽  
Matrix Model ◽  
Wilson Loops ◽  
Expectation Value ◽  
Yang Mills ◽  
Usual Procedure ◽  
Topological Recursion ◽  
Sample Application ◽  
Single Trace ◽  
Genus Expansion

Abstract We consider U(N) $$ \mathcal{N} $$ N = 4 super Yang-Mills theory and discuss how to extract the strong coupling limit of non-planar corrections to observables involving the $$ \frac{1}{2} $$ 1 2 -BPS Wilson loop. Our approach is based on a suitable saddle point treatment of the Eynard-Orantin topological recursion in the Gaussian matrix model. Working directly at strong coupling we avoid the usual procedure of first computing observables at finite planar coupling λ, order by order in 1/N, and then taking the λ ≫ 1 limit. In the proposed approach, matrix model multi-point resolvents take a simplified form and some structures of the genus expansion, hardly visible at low order, may be identified and rigorously proved. As a sample application, we consider the expectation value of multiple coincident circular supersymmetric Wilson loops as well as their correlator with single trace chiral operators. For these quantities we provide novel results about the structure of their genus expansion at large tension, generalising recent results in arXiv:2011.02885.

scholarly journals Phase structure of the quartic-cubic generalized two dimensional Yang-Mills U(N) on the sphere

2008 ◽  
Vol 49 (7) ◽  
pp. 073514
Author(s):  
L. Lavaei-Yanesi ◽  
M. Khorrami
Keyword(s):  
Phase Structure ◽  
Two Dimensional ◽  
Yang Mills

scholarly journals MHV amplitudes in super-Yang–Mills and Wilson Loops

2008 ◽  
Vol 794 (1-2) ◽  
pp. 231-243 ◽  
Author(s):  
Andreas Brandhuber ◽  
Paul Heslop ◽  
Gabriele Travaglini
Keyword(s):  
Wilson Loops ◽  
Yang Mills

scholarly journals Instanton corrections to circular Wilson loops in Script N = 4 Supersymmetric Yang-Mills

2002 ◽  
Vol 2002 (04) ◽  
pp. 040-040 ◽  
Author(s):  
Massimo Bianchi ◽  
Michael B Green ◽  
Stefano Kovacs
Keyword(s):  
Wilson Loops ◽  
Yang Mills

scholarly journals The semiclassical limit of the two‐dimensional quantum Yang–Mills model

1994 ◽  
Vol 35 (10) ◽  
pp. 5354-5361 ◽  
Author(s):  
Christopher King ◽  
Ambar Sengupta
Keyword(s):  
Semiclassical Limit ◽  
Two Dimensional ◽  
Yang Mills
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