scholarly journals The static force from generalized Wilson loops using gradient flow

2022 ◽  
Vol 258 ◽  
pp. 04009
Author(s):  
Viljami Leino ◽  
Nora Brambilla ◽  
Julian Mayer-Steudte ◽  
Antonio Vairo
Keyword(s):  
Wilson Loop ◽  
Finite Size ◽  
Gradient Flow ◽  
Previous Measurement ◽  
Wilson Loops ◽  
Static Force ◽  
Static Potential ◽  
Novel Approach ◽  
Flow Algorithm ◽  
Static Quark

We explore a novel approach to compute the force between a static quark-antiquark pair with the gradient flow algorithm on the lattice. The approach is based on inserting a chromoelectric field in a Wilson loop. The renormalization issues, associated with the finite size of the chromoelectric field on the lattice, can be solved with the use of gradient flow. We compare numerical results for the flowed static potential to our previous measurement of the same observable without a gradient flow.

Motion correction in PET/CT

2005 ◽  
Vol 44 (S 01) ◽  
pp. S46-S50 ◽  
Author(s):  
M. Dawood ◽  
N. Lang ◽  
F. Büther ◽  
M. Schäfers ◽  
O. Schober ◽  
...  
Keyword(s):  
Optical Flow ◽  
Motion Correction ◽  
Motion Vector ◽  
Emission Tomography ◽  
Cardiac Pet ◽  
Novel Approach ◽  
Positron Emission ◽  
Pet Ct ◽  
Flow Algorithm ◽  
Motion Vector Field

Summary:Motion in PET/CT leads to artifacts in the reconstructed PET images due to the different acquisition times of positron emission tomography and computed tomography. The effect of motion on cardiac PET/CT images is evaluated in this study and a novel approach for motion correction based on optical flow methods is outlined. The Lukas-Kanade optical flow algorithm is used to calculate the motion vector field on both simulated phantom data as well as measured human PET data. The motion of the myocardium is corrected by non-linear registration techniques and results are compared to uncorrected images.

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 Determination of α(Mz) from an hyperasymptotic approximation to the energy of a static quark-antiquark pair

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Cesar Ayala ◽  
Xabier Lobregat ◽  
Antonio Pineda
Keyword(s):  
Perturbation Theory ◽  
Energy Range ◽  
Short Distance ◽  
Weak Coupling ◽  
Strong Consistency ◽  
Lattice Data ◽  
Static Potential ◽  
Static Energy ◽  
Static Quark

Abstract We give the hyperasymptotic expansion of the energy of a static quark-antiquark pair with a precision that includes the effects of the subleading renormalon. The terminants associated to the first and second renormalon are incorporated in the analysis when necessary. In particular, we determine the normalization of the leading renormalon of the force and, consequently, of the subleading renormalon of the static potential. We obtain $$ {Z}_3^F $$ Z 3 F (nf = 3) = $$ 2{Z}_3^V $$ 2 Z 3 V (nf = 3) = 0.37(17). The precision we reach in strict perturbation theory is next-to-next-to-next-to-leading logarithmic resummed order both for the static potential and for the force. We find that the resummation of large logarithms and the inclusion of the leading terminants associated to the renormalons are compulsory to get accurate determinations of $$ {\Lambda}_{\overline{\mathrm{MS}}} $$ Λ MS ¯ when fitting to short-distance lattice data of the static energy. We obtain $$ {\Lambda}_{\overline{\mathrm{MS}}}^{\left({n}_f=3\right)} $$ Λ MS ¯ n f = 3 = 338(12) MeV and α(Mz) = 0.1181(9). We have also MS found strong consistency checks that the ultrasoft correction to the static energy can be computed at weak coupling in the energy range we have studied.

scholarly journals Linear confinement and stress-energy tensor around static quark and anti-quark pair -- Lattice simulation with Yang-Mills gradient flow --

2019 ◽  
Author(s):  
Ryosuke Yanagihara ◽  
Takumi Iritani ◽  
Masakiyo Kitazawa ◽  
Masayuki Asakawa ◽  
Tetsuo Hatsuda ◽  
...  
Keyword(s):  
Gradient Flow ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Lattice Simulation ◽  
Yang Mills ◽  
Stress Energy ◽  
Static Quark

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.

SOME WILSON LOOPS IN GRAVITATIONAL METRIC FIELDS

2004 ◽  
Vol 19 (30) ◽  
pp. 5247-5262 ◽  
Author(s):  
D. SHAO ◽  
L. SHAO ◽  
H. NODA ◽  
C. G. SHAO
Keyword(s):  
Cosmic String ◽  
Wilson Loop ◽  
Kerr Metric ◽  
Wilson Loops ◽  
Direction Change ◽  
Leading Term ◽  
Static Sphere

We calculated some Wilson loop functionals in a static sphere-symmetrical diagonal metric field, the Robertson–Walker (RW) metric field and a gravitational metric field established by cosmic string, respectively, and calculated the leading term W(2) and the term W(4) of a Wilson loop in Kerr metric field. Using the direction change of vector when it is parallel transported in the metric field of cosmic string, the cone symmetry of the metric field is demonstrated.

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