Double-winding Wilson loop in SU(N)SU(N) Yang-Mills theory: A criterion for testing the confinement models

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 $C_1$ and $C_2$ are identical, we derive the exact operator relation which relates the double-winding 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 $N \geq 3$, 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 $(N - 3)A_1/(N-1)+A_2$ with $A_1$ and $A_2 (A_1<A_2)$ being the minimal areas spanned respectively by the loops $C_1$ and $C_2$, which is neither sum-of-areas ($A_1+A_2$) nor difference-of-areas ($A_2 - A_1$) law when ($N\geq3$). Indeed, this behavior can be confirmed in the two-dimensional $SU(N)$ Yang-Mills theory exactly.Comment: 6 pages, 2 figures, presented at the 35th International Symposium on Lattice Field Theory (Lattice 2017), 18-24 June 2017, Granada, Spai

Schwinger-Dyson Study for Walking/Conformal Dynamics with IR Cutoffs

Motivated by recent progress on many flavor QCD on a lattice, we investigate conformal/walking dynamics by using Schwinger-Dyson (SD) equation within an improved ladder approximation for two-loop running coupling. By numerically solving the SD equation, we obtain a pole mass $m_{p}$, pion decay constant $f_{\pi}$, and investigate the chiral symmetry breaking and mass anomalous dimension $\gamma_{m}$ in the presence of IR cutoffs $\Lambda_{\mathrm{IR}}$. We find that the chiral symmetry breaking is suppressed \ if IR cutoff $\Lambda_{\mathrm{IR}}$ becomes larger than the critical \ value near the dynamical mass ($\Lambda_{\mathrm{IR}}$ $\simeq m_{D}$) In the conformal phase the $\gamma_{m}$ is strongly suppressed by IR cutoffs for $\Lambda _{\mathrm{IR}}$ $\simeq m_{p}$. We, then, obtain finite size hyperscaling (FSS) relation by adapting a linearized approximation for the SD equation, and examine the $\gamma_{m}$ The results offer valuable insight and suggestion for analyses in lattice gauge theories.Comment: 5 pages,2 figures; Presented at Sakata Memorial KMI Workshop on "Origin of Mass and Strong Coupling Gauge Theories" (SCGT15

The relationship between a topological Yang-Mills field and a magnetic monopole

We show that a Jackiw-Nohl-Rebbi solution, as the most general two-instanton, generates a circular loop of magnetic monopole in four-dimensional Euclidean SU(2) Yang-Mills theory.Comment: 3 pages, 2 figure; to be published in the proceedings of "BARYONS'10", Dec. 7-11, 2010, Osaka, Japa

Quark confinement due to non-Abelian magnetic monopoles in SU(3) Yang-Mills theory

We present recent results on quark confinement: in SU(3) Yang-Mills theory, confinement of fundamental quarks is obtained due to the dual Meissner effect originated from non-Abelian magnetic monopoles defined in a gauge-invariant way, which is distinct from the well-known Abelian projection scenario. This is achieved by using a non-Abelian Stokes theorem for the Wilson loop operator and a new reformulation of the Yang-Mills theory.Comment: 5 pages, 3 eps figures. Talk presented at QCD@Work 2012: International Workshop on QCD - Theory and Experiment, June 18-21, Lecce, Ital

Lattice study of area law for double-winding Wilson loops

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.Comment: 8 pages, 7 figures, presented at the 35th International Symposium on Lattice Field Theory (Lattice 2017), 18-24 June 2017, Granada, Spai