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

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

Unc93B1 Restricts Systemic Lethal Inflammation by Orchestrating Toll-like Receptor 7 and 9 Trafficking

SummaryToll-like receptor-7 (TLR7) and 9, innate immune sensors for microbial RNA or DNA, have been implicated in autoimmunity. Upon activation, TLR7 and 9 are transported from the endoplasmic reticulum (ER) to endolysosomes for nucleic acid sensing by an ER-resident protein, Unc93B1. Little is known, however, about a role for sensor transportation in controlling autoimmunity. TLR9 competes with TLR7 for Unc93B1-dependent trafficking and predominates over TLR7. TLR9 skewing is actively maintained by Unc93B1 and reversed to TLR7 if Unc93B1 loses preferential binding via a D34A mutation. We here demonstrate that mice harboring a D34A mutation showed TLR7-dependent, systemic lethal inflammation. CD4+ T cells showed marked differentiation toward T helper 1 (Th1) or Th17 cell subsets. B cell depletion abolished T cell differentiation and systemic inflammation. Thus, Unc93B1 controls homeostatic TLR7 activation by balancing TLR9 to TLR7 trafficking

Cleavage of Toll-Like Receptor 9 Ectodomain Is Required for In Vivo Responses to Single Strand DNA

Mouse toll-like receptor 9 (TLR9) is an endosomal sensor for single-stranded DNA. TLR9 is transported from the endoplasmic reticulum to endolysosomes by a multiple transmembrane protein Unc93 homolog B1, and proteolytically cleaved at its ectodomain. The structure of TLR9 and its biochemical analyses have shown that the proteolytic cleavage of TLR9 ectodomain enables TLR9-dimerization and TLR9 activation. However, the requirement of TLR9 cleavage in vivo has not been studied. We here show that the 13 amino acids deletion at the cleavage site made TLR9 resistant to proteolytic cleavage. The deletion mutation in the Tlr9 gene impaired TLR9-dependent cytokine production in conventional dendritic cells from the mutant mice. Not only in vitro, in vivo production of inflammatory cytokines (TNF-α and IL-12p40), chemokine (CCR5/RANTES), and type I interferon (IFN-α) induced by administration of TLR9 ligand was also impaired. These results demonstrate that the TLR9 cleavage is required for TLR9 responses in vivo

Coincidence analysis to search for inspiraling compact binaries using TAMA300 and LISM data

Japanese laser interferometric gravitational wave detectors, TAMA300 and LISM, performed a coincident observation during 2001. We perform a coincidence analysis to search for inspiraling compact binaries. The length of data used for the coincidence analysis is 275 hours when both TAMA300 and LISM detectors are operated simultaneously. TAMA300 and LISM data are analyzed by matched filtering, and candidates for gravitational wave events are obtained. If there is a true gravitational wave signal, it should appear in both data of detectors with consistent waveforms characterized by masses of stars, amplitude of the signal, the coalescence time and so on. We introduce a set of coincidence conditions of the parameters, and search for coincident events. This procedure reduces the number of fake events considerably, by a factor $\sim 10^{-4}$ compared with the number of fake events in single detector analysis. We find that the number of events after imposing the coincidence conditions is consistent with the number of accidental coincidences produced purely by noise. We thus find no evidence of gravitational wave signals. We obtain an upper limit of 0.046 /hours (CL $= 90$) to the Galactic event rate within 1kpc from the Earth. The method used in this paper can be applied straightforwardly to the case of coincidence observations with more than two detectors with arbitrary arm directions.Comment: 28 pages, 17 figures, Replaced with the version to be published in Physical Review