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 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.

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 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.

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 Multi-particle finite-volume effects for hexagon tessellations

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Marius de Leeuw ◽  
Burkhard Eden ◽  
Dennis le Plat ◽  
Tim Meier ◽  
Alessandro Sfondrini
Keyword(s):  
Finite Volume ◽  
Correlation Functions ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Volume Effects ◽  
Super Yang Mills Theory

Abstract Correlation functions of gauge-invariant composite operators in $$ \mathcal{N} $$ N = 4 super Yang-Mills theory can be computed by integrability using triangulations. The elementary tile in this process is the hexagon, which should be glued by appropriately inserting resolutions of the identity involving virtual (“mirror”) magnons. We consider this problem for five-point functions of protected operators. At one-loop in the ’t Hooft coupling, it is necessary to glue three adjacent tiles which involves two virtual magnons scattering among each other. We show that the result can be simplified by using an adapted mirror rotation and employing appropriate summation techniques. The mirror-particle contributions then yield hyperlogarithms of weight two. Finally, we use these results to investigate braiding prescriptions introduced in earlier work on the problem.

scholarly journals Relatioship of peaks of correlation functions of amplitude and phase fluctuations with eigen frequencies in oscillation spectrum

2015 ◽  
Vol 1 (3) ◽  
pp. 62-71
Author(s):  
Андрей Поляков ◽  
Andrey Polyakov
Keyword(s):  
Correlation Functions ◽  
Standing Waves ◽  
Cavity Resonator ◽  
Signal Amplitude ◽  
Signal Spectrum ◽  
Universal Relation ◽  
Two Dimensional ◽  
Phase Fluctuations ◽  
One Dimensional ◽  
The Difference

Method of correlation functions of signal amplitude and phase fluctuations (CFAP) is used for processing oscillations in one-dimensional and two-dimensional rectangular cavity resonator models. For all cases, a universal relation, which gives a relationship between the repetition period of peaks on CFAP functions and the difference of adjacent eigenfrequencies in the signal spectrum was obtained. It is shown that for two-dimensional standing wave, this difference can have only two values, each of which corresponds to eigenfrequencies of one-dimensional standing waves. The proposed method allows us to detect all possible one-dimensional standing waves which can occur in the object under study.

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.

COMBINATORIAL POLYNOMIALLY COMPUTABLE CHARACTERISTICS OF SUBSTITUTIONS AND THEIR PROPERTIES

2020 ◽  
Vol 7 (2) ◽  
pp. 34-41
Author(s):  
VLADIMIR NIKONOV ◽  
◽  
ANTON ZOBOV ◽  
Keyword(s):  
Mathematical Expectation ◽  
Point Of View ◽  
Small Range ◽  
Computational Point ◽  
Wide Range ◽  
Bijective Function ◽  
The Difference ◽  
Element Base ◽  
Selection Of

The construction and selection of a suitable bijective function, that is, substitution, is now becoming an important applied task, particularly for building block encryption systems. Many articles have suggested using different approaches to determining the quality of substitution, but most of them are highly computationally complex. The solution of this problem will significantly expand the range of methods for constructing and analyzing scheme in information protection systems. The purpose of research is to find easily measurable characteristics of substitutions, allowing to evaluate their quality, and also measures of the proximity of a particular substitutions to a random one, or its distance from it. For this purpose, several characteristics were proposed in this work: difference and polynomial, and their mathematical expectation was found, as well as variance for the difference characteristic. This allows us to make a conclusion about its quality by comparing the result of calculating the characteristic for a particular substitution with the calculated mathematical expectation. From a computational point of view, the thesises of the article are of exceptional interest due to the simplicity of the algorithm for quantifying the quality of bijective function substitutions. By its nature, the operation of calculating the difference characteristic carries out a simple summation of integer terms in a fixed and small range. Such an operation, both in the modern and in the prospective element base, is embedded in the logic of a wide range of functional elements, especially when implementing computational actions in the optical range, or on other carriers related to the field of nanotechnology.

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