Dirac-mode expansion for confinement and chiral symmetry breaking

We develop a manifestly gauge-covariant expansion and projection using the eigen-mode of the QCD Dirac operator. Applying this method to the Wilson loop and the Polyakov loop, we perform a direct analysis of the correlation between confinement and chiral symmetry breaking in SU(3) lattice QCD calculation on 6^4 at beta=5.6 at the quenched level. Notably, the Wilson loop is found to obey the area law, and the slope parameter corresponding to the string tension or the confinement force is almost unchanged, even after removing the low-lying Dirac modes, which are responsible to chiral symmetry breaking. We find also that the Polyakov loop remains to be almost zero even without the low-lying Dirac modes, which indicates the Z_3-unbroken confinement phase. These results indicate that one-to-one correspondence does not hold between confinement and chiral symmetry breaking in QCD.Comment: 7 pages, 6 figures, Talk given at Conference: Lattice 201

Instantaneous Interquark Potential in Generalized Landau Gauge in SU(3) Lattice QCD: A Linkage between the Landau and the Coulomb Gauges

We investigate in detail "instantaneous interquark potentials", interesting gauge-dependent quantities defined from the spatial correlators of the temporal link-variable $U_4$, in generalized Landau gauge using SU(3) quenched lattice QCD. The instantaneous Q$\bar{\rm Q}$ potential has no linear part in the Landau gauge, and it is expressed by the Coulomb plus linear potential in the Coulomb gauge, where the slope is 2-3 times larger than the physical string tension. Using the generalized Landau gauge, we find that the instantaneous potential can be continuously described between the Landau and the Coulomb gauges, and its linear part rapidly grows in the neighborhood of the Coulomb gauge. We also investigate the instantaneous 3Q potential in the generalized Landau gauge, and obtain similar results to the Q$\bar{\rm Q}$ case. $T$-length terminated Polyakov-line correlators and their corresponding "finite-time potentials" are also investigated in generalized Landau gauge

The crepant transformation conjecture for toric complete intersections

Let X and Y be K-equivalent toric Deligne-Mumford stacks related by a single toric wall-crossing. We prove the Crepant Transformation Conjecture in this case, fully-equivariantly and in genus zero. That is, we show that the equivariant quantum connections for X and Y become gauge-equivalent after analytic continuation in quantum parameters. Furthermore we identify the gauge transformation involved, which can be thought of as a linear symplectomorphism between the Givental spaces for X and Y, with a Fourier-Mukai transformation between the K-groups of X and Y, via an equivariant version of the Gamma-integral structure on quantum cohomology. We prove similar results for toric complete intersections. We impose only very weak geometric hypotheses on X and Y: they can be non-compact, for example, and need not be weak Fano or have Gorenstein coarse moduli space. Our main tools are the Mirror Theorems for toric Deligne-Mumford stacks and toric complete intersections, and the Mellin-Barnes method for analytic continuation of hypergeometric functions

Off-diagonal Gluon Mass Generation and Infrared Abelian Dominance in Maximally Abelian Gauge in SU(3) Lattice QCD

In SU(3) lattice QCD formalism, we propose a method to extract gauge fields from link-variables analytically. With this method, we perform the first study on effective mass generation of off-diagonal gluons and infrared Abelian dominance in the maximally Abelian (MA) gauge in the SU(3) case. Using SU(3) lattice QCD, we investigate the propagator and the effective mass of the gluon fields in the MA gauge with U(1)_3 \timesU(1)_8 Landau gauge fixing. The Monte Carlo simulation is performed on $16^4$ at $\beta$=5.7, 5.8 and 6.0 at the quenched level. The off-diagonal gluons behave as massive vector bosons with the approximate effective mass $M_{\mathrm{off}} \simeq 1.1-1.2\mathrm{GeV}$ in the region of $r =0.3-0.8$fm, and the propagation is limited within a short range, while the propagation of diagonal gluons remains even in a large range. In this way, infrared Abelian dominance is shown in terms of short-range propagation of off-diagonal gluons. Furthermore, we investigate the functional form of the off-diagonal gluon propagator. The functional form is well described by the four-dimensional Euclidean Yukawa-type function $e^{-m_{\rm off}r}/r$ with $m_{\rm off} \simeq 1.3-1.4\mathrm{GeV}$ for $r = 0.1- 0.8$ fm. This also indicates that the spectral function of off-diagonal gluons has the negative-value region

Mirage in Temporal Correlation functions for Baryon-Baryon Interactions in Lattice QCD

Single state saturation of the temporal correlation function is a key condition to extract physical observables such as energies and matrix elements of hadrons from lattice QCD simulations. A method commonly employed to check the saturation is to seek for a plateau of the observables for large Euclidean time. Identifying the plateau in the cases having nearby states, however, is non-trivial and one may even be misled by a fake plateau. Such a situation takes place typically for the system with two or more baryons. In this study, we demonstrate explicitly the danger from a possible fake plateau in the temporal correlation functions mainly for two baryons ($\Xi\Xi$ and $NN$), and three and four baryons ($^3{\rm He}$ and $^4{\rm He})$ as well, employing (2+1)-flavor lattice QCD at $m_{\pi}=0.51$ GeV on four lattice volumes with $L=$ 2.9, 3.6, 4.3 and 5.8 fm. Caution is given for drawing conclusion on the bound $NN$, $3N$ and $4N$ systems only based on the temporal correlation functions.Comment: 32 pages, 13 figures, minor corrections, published version, typos correcte

Hodge-theoretic mirror symmetry for toric stacks

Using the mirror theorem [CCIT15], we give a Landau-Ginzburg mirror description for the big equivariant quantum cohomology of toric Deligne-Mumford stacks. More precisely, we prove that the big equivariant quantum D-module of a toric Deligne-Mumford stack is isomorphic to the Saito structure associated to the mirror Landau-Ginzburg potential. We give a GKZ-style presentation of the quantum D-module, and a combinatorial description of quantum cohomology as a quantum Stanley-Reisner ring. We establish the convergence of the mirror isomorphism and of quantum cohomology in the big and equivariant setting

Precise Determination of Blackbody Radiation Shifts in a Strontium Molecular Lattice Clock

Molecular lattice clocks enable the search for new physics, such as fifth forces or temporal variations of fundamental constants, in a manner complementary to atomic clocks. Blackbody radiation (BBR) is a major contributor to the systematic error budget of conventional atomic clocks and is notoriously difficult to characterize and control. Here, we combine infrared Stark-shift spectroscopy in a molecular lattice clock and modern quantum chemistry methods to characterize the polarizabilities of the Sr$_2$ molecule from dc to infrared. Using this description, we determine the static and dynamic blackbody radiation shifts for all possible vibrational clock transitions to the $10^{-16}$ level. This constitutes an important step towards mHz-level molecular spectroscopy in Sr$_2$, and provides a framework for evaluating BBR shifts in other homonuclear molecules.Comment: 6 pages, 4 figures, updated reference

LEUKEMIA-ASSOCIATED TRANSPLANTATION ANTIGENS RELATED TO MURINE LEUKEMIA VIRUS : THE X.1 SYSTEM: IMMUNE RESPONSE CONTROLLED BY A LOCUS LINKED TOH-2

Two BALB radiation leukemias are strongly rejected by hybrids of BALB with certain other mouse strains, although BALB mice themselves exhibit no detectable resistance whatever. Hybrids immunized with progressively increased inocula are resistant to 200 x 106 or more leukemia cells; their serum is cytotoxic for the leukemia cells in vitro and protects BALB mice against challenge with these BALB leukemias. The antigenic system thus identified has been named X.1. In (BALB x B6) hybrids the major determinant of resistance was shown to be a B6 gene in the K region of H-2. This is likely to be the Rgv-1 (Resistance to gross virus) locus of Lilly, which may thus be identified in this case as an Ir (Immune response) allele conferring ability to respond to X.1 antigen on MuLV and leukemia cells, and so responsible for production of X.1 antibody and the rejection of X.1+ leukemia cells by hybrid mice. Immunoelectron microscopy with X.1 antiserum (from immunized hybrids) shows labeling both on the cell surface and on virions produced by the leukemia cells. It is not known whether X.1 comprises only one or more than one antigen. Three radiation-induced BALB leukemias, one A strain radiation-induced leukemia, and 15/15 AKR primary spontaneous leukemias were typed X.1+ by the cytotoxicity test. Several other leukemias, including one induced by passage A Gross virus and one long-transplanted AKR ascites leukemia carried in (B6 x AKR)F1 hybrids, were X.1-. Normal mice of strains with a high incidence of leukemia and one other strain (129) express X.1 antigen, but evidently in amounts too small for certain detection in vitro; by the method of absorption in vivo, however, these strains could be typed X.1+ and other strains X.1-. We ascribe the X.1 antigen system tentatively to a sub-type of MuLV that is not passage A Gross virus and is probably not the dominant sub-type in strains with a high incidence of leukemia. After repeated passage in hybrids, one of the BALB leukemias became relatively resistant to rejection by the hybrid, partially lost its sensitivity to X.1 antiserum in vitro, and in electron micrographs was seen to produce fewer virions. The serum of untreated (BALB x B6) hybrids often contains cytotoxic antibody against leukemia cells, some of it probably anti-X.1. But another commonly occurring antibody, which is cytotoxic for C57BL leukemia EL4, appears to belong to another (undefined) system

Mirror Map as Generating Function of Intersection Numbers: Toric Manifolds with Two K\"ahler Forms

In this paper, we extend our geometrical derivation of expansion coefficients of mirror maps by localization computation to the case of toric manifolds with two K\"ahler forms. Especially, we take Hirzebruch surfaces F_{0}, F_{3} and Calabi-Yau hypersurface in weighted projective space P(1,1,2,2,2) as examples. We expect that our results can be easily generalized to arbitrary toric manifold.Comment: 45 pages, 2 figures, minor errors are corrected, English is refined. Section 1 and Section 2 are enlarged. Especially in Section 2, confusion between the notion of resolution and the notion of compactification is resolved. Computation under non-zero equivariant parameters are added in Section

A terahertz vibrational molecular clock with systematic uncertainty at the 10−1410^{-14} level

Neutral quantum absorbers in optical lattices have emerged as a leading platform for achieving clocks with exquisite spectroscopic resolution. However, the studies of these clocks and their systematic shifts have so far been limited to atoms. Here, we extend this architecture to an ensemble of diatomic molecules and experimentally realize an accurate lattice clock based on pure molecular vibration. We evaluate the leading systematics, including the characterization of nonlinear trap-induced light shifts, achieving a total systematic uncertainty of $4.6\times10^{-14}$. The absolute frequency of the vibrational splitting is measured to be 31 825 183 207 592.8(5.1) Hz, enabling the dissociation energy of our molecule to be determined with record accuracy. Our results represent an important milestone in molecular spectroscopy and THz-frequency standards, and may be generalized to other neutral molecular species with applications for fundamental physics, including tests of molecular quantum electrodynamics and the search for new interactions.Comment: 17 pages, 8 figure