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

Fast Vacuum Decay into Quark Pairs in Strong Color Electric and Magnetic Fields

We study quark-pair creations in strong color electromagnetic fields. We point out that, for massless quarks, the vacuum persistency probability per unit space-time volume is zero, i.e., the quark-pair creation rate w is infinite, in general homogeneous color electromagnetic fields, while it is finite when the color magnetic field is absent. We find that the contribution from the lowest Landau level (LLL) dominates this phenomenon. With an effective theory of the LLL projection, we also discuss dynamics of the vacuum decay, taking into account the back reaction of pair creations.Comment: 4 pages, 1 figure, contribution to the proceedings of International conference on the structure of baryons (BARYONS'10), RCNP, Osaka, Japan, Dec. 7-11, 2010; fig.2 delete

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

Gluon-propagator functional form in the Landau gauge in SU(3) lattice QCD: Yukawa-type gluon propagator and anomalous gluon spectral function

We study the gluon propagator $D_{\mu\nu}^{ab}(x)$ in the Landau gauge in SU(3) lattice QCD at $\beta$ = 5.7, 5.8, and 6.0 at the quenched level. The effective gluon mass is estimated as $400 \sim 600$MeV for $r \equiv (x_\alpha x_\alpha)^{1/2} = 0.5 \sim 1.0$ fm. Through the functional-form analysis of $D_{\mu\nu}^{ab}(x)$ obtained in lattice QCD, we find that the Landau-gauge gluon propagator $D_{\mu\mu}^{aa}(r)$ is well described by the Yukawa-type function $e^{-mr}/r$ with $m \simeq 600$MeV for $r = 0.1 \sim 1.0$ fm in the four-dimensional Euclidean space-time. In the momentum space, the gluon propagator $\tilde D_{\mu\mu}^{aa}(p^2)$ with $(p^2)^{1/2}= 0.5 \sim 3$ GeV is found to be well approximated with a new-type propagator of $(p^2+m^2)^{-3/2}$, which corresponds to the four-dimensional Yukawa-type propagator. Associated with the Yukawa-type gluon propagator, we derive analytical expressions for the zero-spatial-momentum propagator $D_0(t)$, the effective mass $M_{\rm eff}(t)$, and the spectral function $\rho(\omega)$ of the gluon field. The mass parameter $m$ turns out to be the effective gluon mass in the infrared region of $\sim$ 1fm. As a remarkable fact, the obtained gluon spectral function $\rho(\omega)$ is almost negative-definite for $\omega >m$, except for a positive $\delta$-functional peak at $\omega=m$.Comment: 20 pages, 15 figure

On the Crepant Resolution Conjecture in the Local Case

In this paper we analyze four examples of birational transformations between local Calabi-Yau 3-folds: two crepant resolutions, a crepant partial resolution, and a flop. We study the effect of these transformations on genus-zero Gromov-Witten invariants, proving the Coates-Corti-Iritani-Tseng/Ruan form of the Crepant Resolution Conjecture in each case. Our results suggest that this form of the Crepant Resolution Conjecture may also hold for more general crepant birational transformations. They also suggest that Ruan's original Crepant Resolution Conjecture should be modified, by including appropriate "quantum corrections", and that there is no straightforward generalization of either Ruan's original Conjecture or the Cohomological Crepant Resolution Conjecture to the case of crepant partial resolutions. Our methods are based on mirror symmetry for toric orbifolds.Comment: 27 pages. This is a substantially revised and shortened version of my preprint "Wall-Crossings in Toric Gromov-Witten Theory II: Local Examples"; all results contained here are also proved there. To appear in Communications in Mathematical Physic

Enumerative aspects of the Gross-Siebert program

We present enumerative aspects of the Gross-Siebert program in this introductory survey. After sketching the program's main themes and goals, we review the basic definitions and results of logarithmic and tropical geometry. We give examples and a proof for counting algebraic curves via tropical curves. To illustrate an application of tropical geometry and the Gross-Siebert program to mirror symmetry, we discuss the mirror symmetry of the projective plane.Comment: A version of these notes will appear as a chapter in an upcoming Fields Institute volume. 81 page

Lagrangian Floer superpotentials and crepant resolutions for toric orbifolds

We investigate the relationship between the Lagrangian Floer superpotentials for a toric orbifold and its toric crepant resolutions. More specifically, we study an open string version of the crepant resolution conjecture (CRC) which states that the Lagrangian Floer superpotential of a Gorenstein toric orbifold $\mathcal{X}$ and that of its toric crepant resolution $Y$ coincide after analytic continuation of quantum parameters and a change of variables. Relating this conjecture with the closed CRC, we find that the change of variable formula which appears in closed CRC can be explained by relations between open (orbifold) Gromov-Witten invariants. We also discover a geometric explanation (in terms of virtual counting of stable orbi-discs) for the specialization of quantum parameters to roots of unity which appears in Y. Ruan's original CRC ["The cohomology ring of crepant resolutions of orbifolds", Gromov-Witten theory of spin curves and orbifolds, 117-126, Contemp. Math., 403, Amer. Math. Soc., Providence, RI, 2006]. We prove the open CRC for the weighted projective spaces $\mathcal{X}=\mathbb{P}(1,\ldots,1,n)$ using an equality between open and closed orbifold Gromov-Witten invariants. Along the way, we also prove an open mirror theorem for these toric orbifolds.Comment: 48 pages, 1 figure; v2: references added and updated, final version, to appear in CM

The Infrared Behaviour of the Pure Yang-Mills Green Functions

We review the infrared properties of the pure Yang-Mills correlators and discuss recent results concerning the two classes of low-momentum solutions for them reported in literature; i.e. decoupling and scaling solutions. We will mainly focuss on the Landau gauge and pay special attention to the results inferred from the analysis of the Dyson-Schwinger equations of the theory and from "{\it quenched}" lattice QCD. The results obtained from properly interplaying both approaches are strongly emphasized.Comment: Final version to be published in FBS (54 pgs., 11 figs., 4 tabs

Excited States in 52Fe and the Origin of the Yrast Trap at I=12+

Excited states in 52Fe have been determined up to spin 10\hbar in the reaction 28Si + 28Si at 115 MeV by using \gamma-ray spectroscopy methods at the GASP array. The excitation energy of the yrast 10+ state has been determined to be 7.381 MeV, almost 0.5 MeV above the well known \beta+-decaying yrast 12+ state, definitely confirming the nature of its isomeric character. The mean lifetimes of the states have been measured by using the Doppler Shift Attenuation method. The experimental data are compared with spherical shell model calculations in the full pf-shell.Comment: 9 pages, RevTeX, 7 figures include