ASYMPTOTIC AdS STRING SOLUTIONS FOR NULL POLYGONAL WILSON LOOPS IN R1,2

2010 ◽  
Vol 25 (30) ◽  
pp. 2555-2569 ◽  
Author(s):  
SHIJONG RYANG
Keyword(s):  
Asymptotic Behavior ◽  
Strong Coupling ◽  
Wilson Loop ◽  
Scattering Amplitude ◽  
Wilson Loops ◽  
String Solution ◽  
Reality Condition ◽  
Linear Problems ◽  
Two Parameters

For the asymptotic string solution in AdS3 which is represented by the AdS3 Poincaré coordinates and yields the planar multi-gluon scattering amplitude at strong coupling in arXiv:0904.0663, we express it by the AdS4 Poincaré coordinates and demonstrate that the hexagonal and octagonal Wilson loops surrounding the string surfaces take closed contours consisting of null vectors in R1,2 owing to the relations of Stokes matrices. For the tetragonal Wilson loop we construct a string solution characterized by two parameters by solving the auxiliary linear problems and demanding a reality condition, and analyze the asymptotic behavior of the solution in R1,2. The freedoms of two parameters are related with some conformal SO(2,4) transformations.

scholarly journals Lattice study of area law for double-winding Wilson loops

2018 ◽  
Vol 175 ◽  
pp. 12010
Author(s):  
Akihiro Shibata ◽  
Seikou Kato ◽  
Kei-Ichi Kondo ◽  
Ryutaro Matsudo
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Strong Coupling ◽  
Wilson Loop ◽  
Strong Coupling Expansion ◽  
Wilson Loops ◽  
Yang Mills ◽  
Lattice Monte Carlo ◽  
Area Law

We study the double-winding Wilson loops in the SU(N) Yang-Mills theory on the lattice. We discuss how the area law falloff of the double-winding Wilson loop average is modified by changing the enclosing contours C1 and C2 for various values of the number of color N. By using the strong coupling expansion, we evaluate the double-winding Wilson loop average in the lattice SU(N) Yang-Mills theory. Moreover, we compute the double-winding Wilson loop average by lattice Monte Carlo simulations for SU(2) and SU(3). We further discuss the results from the viewpoint of the Non-Abelian Stokes theorem in the higher representations.

scholarly journals On the structure of non-planar strong coupling corrections to correlators of BPS Wilson loops and chiral primary operators

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
M. Beccaria ◽  
A. A. Tseytlin
Keyword(s):  
Strong Coupling ◽  
Wilson Loop ◽  
Root Function ◽  
String Tension ◽  
Wilson Loops ◽  
Square Root ◽  
Abjm Theory ◽  
Hooft Coupling ◽  
Higher Genus ◽  
Coupling Terms

Abstract Starting with some known localization (matrix model) representations for correlators involving 1/2 BPS circular Wilson loop $$ \mathcal{W} $$ W in $$ \mathcal{N} $$ N = 4 SYM theory we work out their 1/N expansions in the limit of large ’t Hooft coupling λ. Motivated by a possibility of eventual matching to higher genus corrections in dual string theory we follow arXiv:2007.08512 and express the result in terms of the string coupling $$ {g}_{\mathrm{s}}\sim {g}_{\mathrm{YM}}^2\sim \lambda /N $$ g s ∼ g YM 2 ∼ λ / N and string tension $$ T\sim \sqrt{\lambda } $$ T ∼ λ . Keeping only the leading in 1/T term at each order in gs we observe that while the expansion of $$ \left\langle \mathcal{W}\right\rangle $$ W is a series in $$ {g}_{\mathrm{s}}^2/T $$ g s 2 / T , the correlator of the Wilson loop with chiral primary operators $$ {\mathcal{O}}_J $$ O J has expansion in powers of $$ {g}_{\mathrm{s}}^2/{T}^2 $$ g s 2 / T 2 . Like in the case of $$ \left\langle \mathcal{W}\right\rangle $$ W where these leading terms are known to resum into an exponential of a “one-handle” contribution $$ \sim {g}_{\mathrm{s}}^2/T $$ ∼ g s 2 / T , the leading strong coupling terms in $$ \left\langle {\mathcal{WO}}_J\right\rangle $$ WO J sum up to a simple square root function of $$ {g}_{\mathrm{s}}^2/{T}^2 $$ g s 2 / T 2 . Analogous expansions in powers of $$ {g}_{\mathrm{s}}^2/T $$ g s 2 / T are found for correlators of several coincident Wilson loops and they again have a simple resummed form. We also find similar expansions for correlators of coincident 1/2 BPS Wilson loops in the ABJM theory.

scholarly journals Symmetric Wilson Loops beyond leading order

2016 ◽  
Vol 1 (2) ◽  
Author(s):  
Xinyi Chen-Lin
Keyword(s):  
Strong Coupling ◽  
Wilson Loop ◽  
Order Term ◽  
Exact Result ◽  
Wilson Loops ◽  
Leading Order ◽  
Fundamental Representation ◽  
Symmetric Representation ◽  
Yang Mills

We study the circular Wilson loop in the symmetric representation of U(N)U(N) in mathcal{N} = 4𝒩=4 super-Yang-Mills (SYM). In the large NN limit, we computed the exponentially-suppressed corrections for strong coupling, which suggests non-perturbative physics in the dual holographic theory. We also computed the next-to-leading order term in 1/N1/N, and the result matches with the exact result from the kk-fundamental representation.

TOPOLOGY OF THE GRASSMANNIAN σ MODEL ON A LATTICE

1987 ◽  
Vol 02 (08) ◽  
pp. 601-608 ◽  
Author(s):  
T. FUKAI ◽  
M. V. ATRE
Keyword(s):  
Partition Function ◽  
Strong Coupling ◽  
Wilson Loop ◽  
Strong Coupling Limit ◽  
Topological Term

The Grassmannian σ model with a topological term is studied on a lattice. The θ dependence of the partition function and the Wilson loop are evaluated in the strong coupling limit. The latter is shown to be independent of the area at θ = π, as in the CPN−1 model.

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 Mocking the u-plane integral

2021 ◽  
Vol 8 (3) ◽  
Author(s):  
Georgios Korpas ◽  
Jan Manschot ◽  
Gregory W. Moore ◽  
Iurii Nidaiev
Keyword(s):  
Asymptotic Behavior ◽  
Gauge Theory ◽  
Entire Function ◽  
Gauge Group ◽  
Strong Coupling ◽  
Modular Forms ◽  
Correlation Functions ◽  
Coulomb Branch ◽  
Mock Modular Forms ◽  
Donaldson Invariants

AbstractThe u-plane integral is the contribution of the Coulomb branch to correlation functions of $${\mathcal {N}}=2$$ N = 2 gauge theory on a compact four-manifold. We consider the u-plane integral for correlators of point and surface observables of topologically twisted theories with gauge group $$\mathrm{SU}(2)$$ SU ( 2 ) , for an arbitrary four-manifold with $$(b_1,b_2^+)=(0,1)$$ ( b 1 , b 2 + ) = ( 0 , 1 ) . The u-plane contribution equals the full correlator in the absence of Seiberg–Witten contributions at strong coupling, and coincides with the mathematically defined Donaldson invariants in such cases. We demonstrate that the u-plane correlators are efficiently determined using mock modular forms for point observables, and Appell–Lerch sums for surface observables. We use these results to discuss the asymptotic behavior of correlators as function of the number of observables. Our findings suggest that the vev of exponentiated point and surface observables is an entire function of the fugacities.

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.

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