MHV amplitudes in super-Yang–Mills and Wilson Loops

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.

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

Journal of High Energy Physics ◽

10.1007/jhep04(2021)194 ◽

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

Journal of High Energy Physics ◽

10.1088/1126-6708/2002/04/040 ◽

2002 ◽

Vol 2002 (04) ◽

pp. 040-040 ◽

Cited By ~ 39

Author(s):

Massimo Bianchi ◽

Michael B Green ◽

Stefano Kovacs

Keyword(s):

Wilson Loops ◽

Yang Mills

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Hedgehogs in Wilson loops and phase transition in SU(2) Yang–Mills theory

Nuclear Physics B ◽

10.1016/j.nuclphysb.2006.05.017 ◽

2006 ◽

Vol 748 (3) ◽

pp. 524-539 ◽

Cited By ~ 5

Author(s):

V.A. Belavin ◽

M.N. Chernodub ◽

I.E. Kozlov

Keyword(s):

Phase Transition ◽

Wilson Loops ◽

Yang Mills

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NULL ZIG-ZAG WILSON LOOPS IN $\mathcal{N}=4$ SYM

Modern Physics Letters A ◽

10.1142/s0217732310032093 ◽

2010 ◽

Vol 25 (08) ◽

pp. 627-639

Author(s):

ZHIFENG XIE

Keyword(s):

Perturbation Theory ◽

Wilson Loop ◽

Wilson Loops ◽

Finite Part ◽

Expectation Value ◽

Line Segments ◽

Yang Mills ◽

Circular Shape ◽

The One ◽

Arbitrary Shapes

In planar [Formula: see text] supersymmetric Yang–Mills theory we have studied one kind of (locally) BPS Wilson loops composed of a large number of light-like segments, i.e. null zig-zags. These contours oscillate around smooth underlying spacelike paths. At one-loop in perturbation theory, we have compared the finite part of the expectation value of null zig-zags to the finite part of the expectation value of non-scalar-coupled Wilson loops whose contours are the underlying smooth spacelike paths. In arXiv:0710.1060 [hep-th] it was argued that these quantities are equal for the case of a rectangular Wilson loop. Here we present a modest extension of this result to zig-zags of circular shape and zig-zags following non-parallel, disconnected line segments and show analytically that the one-loop finite part is indeed that given by the smooth spacelike Wilson loop without coupling to scalars which the zig-zag contour approximates. We make some comments regarding the generalization to arbitrary shapes.

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Twistor Parametrization of Locally BPS Super-Wilson Loops

Advances in Mathematical Physics ◽

10.1155/2017/4852015 ◽

2017 ◽

Vol 2017 ◽

pp. 1-9 ◽

Cited By ~ 1

Author(s):

Cristian Vergu

Keyword(s):

Correlation Function ◽

Wilson Loop ◽

Point Of View ◽

Scalar Coupling ◽

Wilson Loops ◽

Yang Mills ◽

The One

We consider the kinematics of the locally BPS super-Wilson loop in N=4 super-Yang-Mills with scalar coupling from a twistorial point of view. We find that the kinematics can be described either as supersymmetrized pure spinors or as a point in the product of two super-Grassmannian manifolds G2∣2(4∣4)×G2∣2(4∣4). In this description of the kinematics the scalar–scalar correlation function appearing in the one-loop evaluation of the super-Wilson loop can be neatly written as a sum of four superdeterminants.

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