scholarly journals Twistor Parametrization of Locally BPS Super-Wilson Loops

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
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.

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

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.

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 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 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 POTENTIAL ENERGY OF YANG–MILLS VORTICES IN THREE AND FOUR DIMENSIONS

1999 ◽  
Vol 14 (25) ◽  
pp. 1725-1732 ◽  
Author(s):  
DMITRI DIAKONOV
Keyword(s):  
Magnetic Flux ◽  
Potential Energy ◽  
Wilson Loop ◽  
Parallel Line ◽  
Vortex Center ◽  
Four Dimensions ◽  
Yang Mills ◽  
Loop Approximation ◽  
The One

We calculate the energy of a Yang–Mills vortex as function of its magnetic flux or as the Wilson loop surrounding the vortex center. The calculation is performed in the one-loop approximation. A parallel line with a potential as function of the Polyakov at nonzero temperatures is drawn. We find that quantized Z(2) vortices are dynamically preferred though vortices with arbitrary fluxes cannot be ruled out.

scholarly journals Giant Wilson loops and AdS2/dCFT1

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Simone Giombi ◽  
Jiaqi Jiang ◽  
Shota Komatsu
Keyword(s):  
Correlation Functions ◽  
Wilson Loop ◽  
Wilson Loops ◽  
One Dimensional ◽  
Yang Mills ◽  
Large Rank ◽  
Hooft Coupling ◽  
Multiple Integrals ◽  
The Difference ◽  
Selection Of

Abstract The 1/2-BPS Wilson loop in $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory is an important and well-studied example of conformal defect. In particular, much work has been done for the correlation functions of operator insertions on the Wilson loop in the fundamental representation. In this paper, we extend such analyses to Wilson loops in the large-rank symmetric and antisymmetric representations, which correspond to probe D3 and D5 branes with AdS2× S2 and AdS2× S4 worldvolume geometries, ending at the AdS5 boundary along a one-dimensional contour. We first compute the correlation functions of protected scalar insertions from supersymmetric localization, and obtain a representation in terms of multiple integrals that are similar to the eigenvalue integrals of the random matrix, but with important differences. Using ideas from the Fermi Gas formalism and the Clustering method, we evaluate their large N limit exactly as a function of the ’t Hooft coupling. The results are given by simple integrals of polynomials that resemble the Q-functions of the Quantum Spectral Curve, with integration measures depending on the number of insertions. Next, we study the correlation functions of fluctuations on the probe D3 and D5 branes in AdS. We compute a selection of three- and four-point functions from perturbation theory on the D-branes, and show that they agree with the results of localization when restricted to supersymmetric kinematics. We also explain how the difference of the internal geometries of the D3 and D5 branes manifests itself in the localization computation.

scholarly journals ${\mathcal N}=1^*$ MODEL SUPERPOTENTIAL REVISITED (IR BEHAVIOR OF ${\mathcal N}=4$ LIMIT)

2007 ◽  
Vol 22 (28) ◽  
pp. 5089-5115 ◽  
Author(s):  
S. ARNONE ◽  
G. DI SEGNI ◽  
M. SICCARDI ◽  
K. YOSHIDA
Keyword(s):  
Field Theory ◽  
Point Of View ◽  
Theory Method ◽  
Loop Contribution ◽  
Yang Mills ◽  
The Matrix ◽  
Group Variation ◽  
The One ◽  
Elementary Field ◽  
Model Point

The one-loop contribution to the superpotential, in particular the Veneziano–Yankielowicz potential in [Formula: see text] supersymmetric Yang–Mills model is discussed from an elementary field theory method and the matrix model point of view. Both approaches are based on the renormalization group variation of the superconformal [Formula: see text] supersymmetric Yang–Mills model.

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.

Understanding functional illiteracy from a policy, adult education, and cognition point of view: Towards a joint referent framework

2019 ◽  
Vol 30 (2) ◽  
pp. 109-122
Author(s):  
Aleksandar Bulajić ◽  
Miomir Despotović ◽  
Thomas Lachmann
Keyword(s):  
Adult Education ◽  
Operational Definition ◽  
Literacy Skills ◽  
Point Of View ◽  
Industrialized Countries ◽  
Functional Illiteracy ◽  
Scale Levels ◽  
Components Of Reading ◽  
The One ◽  
Definition Of

Abstract. The article discusses the emergence of a functional literacy construct and the rediscovery of illiteracy in industrialized countries during the second half of the 20th century. It offers a short explanation of how the construct evolved over time. In addition, it explores how functional (il)literacy is conceived differently by research discourses of cognitive and neural studies, on the one hand, and by prescriptive and normative international policy documents and adult education, on the other hand. Furthermore, it analyses how literacy skills surveys such as the Level One Study (leo.) or the PIAAC may help to bridge the gap between cognitive and more practical and educational approaches to literacy, the goal being to place the functional illiteracy (FI) construct within its existing scale levels. It also sheds more light on the way in which FI can be perceived in terms of different cognitive processes and underlying components of reading. By building on the previous work of other authors and previous definitions, the article brings together different views of FI and offers a perspective for a needed operational definition of the concept, which would be an appropriate reference point for future educational, political, and scientific utilization.

Recommendations of The Ombudsman’s Dilemma: Between Law Enforcement Officials and Protection of Credibility

2018 ◽  
Vol 2 ◽  
pp. 1-12
Author(s):  
Dyah Adriantini Sintha Dewi
Keyword(s):  
Law Enforcement ◽  
Public Service ◽  
Public Services ◽  
Point Of View ◽  
Law Enforcement Officials ◽  
Muslim Majority ◽  
The Republic ◽  
The Government ◽  
The One ◽  
Oversight Body

The Ombudsman as an external oversight body for official performance, in Fikih Siyasah (constitutionality in Islam) is included in the supervision stipulated in legislation (al-musahabah al-qomariyah). Supervision is done so that public service delivery to the community is in accordance with the rights of the community. This is done because in carrying out its duties, officials are very likely to conduct mal administration, which is bad public services that cause harm to the community. The Ombudsman is an institution authorized to resolve the mal administration issue, in which one of its products is by issuing a recommendation. Although Law No. 37 of 2018 on the Ombudsman of the Republic of Indonesia states that the recommendation is mandatory, theombudsman's recommendations have not been implemented. This is due to differences in point of view, ie on the one hand in the context of law enforcement, but on the other hand the implementation of the recommendation is considered as a means of opening the disgrace of officials. Recommendations are the last alternative of Ombudsman's efforts to resolve the mal administration case, given that a win-win solution is the goal, then mediation becomes the main effort. This is in accordance with the condition of the Muslim majority of Indonesian nation and prioritizes deliberation in resolving dispute. Therefore, it is necessary to educate the community and officials related to the implementation of the Ombudsman's recommendations in order to provide good public services for the community, which is the obligation of the government.

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