Cutoff Effects on Energy-Momentum Tensor Correlators in Lattice Gauge Theory

We investigate the discretization errors affecting correlators of the energy-momentum tensor $T_{\mu\nu}$ at finite temperature in SU($N_c$) gauge theory with the Wilson action and two different discretizations of $T_{\mu\nu}$. We do so by using lattice perturbation theory and non-perturbative Monte-Carlo simulations. These correlators, which are functions of Euclidean time $x_0$ and spatial momentum ${\bf p}$, are the starting point for a lattice study of the transport properties of the gluon plasma. We find that the correlator of the energy $\int d^3x T_{00}$ has much larger discretization errors than the correlator of momentum $\int d^3x T_{0k}$. Secondly, the shear and diagonal stress correlators ($T_{12}$ and $T_{kk}$) require \Nt\geq 8 for the $Tx_0={1/2}$ point to be in the scaling region and the cutoff effect to be less than 10%. We then show that their discretization errors on an anisotropic lattice with \as/\at=2 are comparable to those on the isotropic lattice with the same temporal lattice spacing. Finally, we also study finite ${\bf p}$ correlators.Comment: 16 pages, 5 figure

Glueballs and the Pomeron

We present our latest results on the glueball spectrum of SU(N) gauge theories in 2+1 dimensions for spins ranging from 0 to 6 inclusive, as well as preliminary results for SU(3) in 3+1 dimensions. Simple glueball models and the relation of the even-spin spectrum to the 'Pomeron' are discussed.Comment: LAT03 proceedings (spectrum), 3 pages, 3 figures, talk by H.Meye

Locality and Statistical Error Reduction on Correlation Functions

We propose a multilevel Monte-Carlo scheme, applicable to local actions, which is expected to reduce statistical errors on correlation functions. We give general arguments to show how the efficiency and parameters of the algorithm are determined by the low-energy spectrum. As an application, we measure the euclidean-time correlation of pairs of Wilson loops in SU(3) pure gauge theory with constant relative errors. In this case the ratio of the new method's efficiency to the standard one increases as exp{m_0t/2}, where m_0 is the mass gap and t the time separation.Comment: One paragraph changed in the introduction; some misprints corrected; 12 pages, 6 figure

Glueball matrix elements: a lattice calculation and applications

We compute the matrix elements of the energy-momentum tensor between glueball states and the vacuum in SU(3) lattice gauge theory and extrapolate them to the continuum. These matrix elements may play an important phenomenological role in identifying glue-rich mesons. Based on a relation derived long ago by the ITEP group for J/psi radiative decays, the scalar matrix element leads to a branching ratio for the glueball that is at least three times larger than the experimentally observed branching ratio for the f_0 mesons above 1GeV. This suggests that the glueball component must be diluted quite strongly among the known scalar mesons. Finally we review the current best continuum determination of the scalar and tensor glueball masses, the deconfining temperature, the string tension and the Lambda parameter, all in units of the Sommer reference scale, using calculations based on the Wilson action.Comment: 14 pages, 4 figure

Spatial correlators in strongly coupled plasmas

We numerically calculate the spatial correlators of the scalar and pseudoscalar operators $F^2$ and $F\tilde F$, in SU(3) Yang-Mills theory at zero and finite-temperature on the lattice. We compare the results over the distances $\frac{1}{2T}<r<\frac{3}{2T}$ to the free-field prediction, to the operator-product expansion as well as to the strongly coupled large-$N_c$ \sN=4 super-Yang-Mills theory, where results are obtained by AdS/CFT methods. For $T_c<T<1.15T_c$, both channels exhibit stronger spatial correlations than in the vacuum, and we give an explanation for this, using sum-rules and the operator-product expansion. The AdS/CFT calculation provides a semi-quantitatively successful description of the vacuum-subtracted $F^2$ correlator, renormalized in the 3-loop $\overline{\rm MS}$ scheme, in the interval of temperatures $1.2<T/T_c<1.9$, while the free-field prediction has the wrong sign. The $F\tilde F$ and $F^2$ correlators are predicted to have the same functional form both at weak coupling and in the strongly coupled SYM theory. The Yang-Mills plasma does not meet that expectation below $2T_c$. Instead we find that strong fluctuations of $F\tilde F$ are present at least up to that temperature. We discuss the impact of our results on our understanding of the quark-gluon plasma.Comment: 32 pages, 9 figures, 4 tables; added some references, more detailed captions, conclusions unchange

Plaquette expectation value and lattice free energy of three-dimensional SU(N) gauge theory

We use high precision lattice simulations to calculate the plaquette expectation value in three-dimensional SU(N) gauge theory for N=2,3,4,5,8. Using these results, we study the N-dependence of the first non-perturbative coefficient in the weak-coupling expansion of hot QCD. We demonstrate that, in the limit of large N, the functional form of the plaquette expectation value with ultraviolet divergences subtracted is 15.9(2)-44(2)/N^2.Comment: 14 pages, 6 figures. v2: references added; published versio

Glueballs and k-strings in SU(N) gauge theories : calculations with improved operators

We test a variety of blocking and smearing algorithms for constructing glueball and string wave-functionals, and find some with much improved overlaps onto the lightest states. We use these algorithms to obtain improved results on the tensions of k-strings in SU(4), SU(6), and SU(8) gauge theories. We emphasise the major systematic errors that still need to be controlled in calculations of heavier k-strings, and perform calculations in SU(4) on an anisotropic lattice in a bid to minimise one of these. All these results point to the k-string tensions lying part-way between the `MQCD' and `Casimir Scaling' conjectures, with the power in 1/N of the leading correction lying in [1,2]. We also obtain some evidence for the presence of quasi-stable strings in calculations that do not use sources, and observe some near-degeneracies between (excited) strings in different representations. We also calculate the lightest glueball masses for N=2, ...,8, and extrapolate to N=infinity, obtaining results compatible with earlier work. We show that the N=infinity factorisation of the Euclidean correlators that are used in such mass calculations does not make the masses any less calculable at large N.Comment: 49 pages, 15 figure

An update on the status of wet forest stream-dwelling frogs of the Eungella region

Eungella’s wet forests are home to a number of stream-breeding frogs including three species endemic to the Eungella region: the Eungella dayfrog (Taudactylus eungellensis), Eungella tinkerfrog (T. liemi), and northern gastric brooding frog (Rheobatrachus vitellinus). During the mid-1980s, T. eungellensis and R. vitellinus suffered dramatic population declines attributable to amphibian chytridiomycosis, a disease caused by the amphibian chytrid fungus (Batrachochytrium dendrobatidis or Bd). While surveys in the late 1980s failed to locate T. eungellensis or R. vitellinus, populations of the former were located on a handful of streams surveyed by researchers in the mid-to-late 1990s. Between January 2000 and November 2015, additional surveys targeting these and other wet forest frog species were conducted at 114 sites within Eungella National Park and adjoining areas of State Forest. During these surveys, we located T. eungellensis at many more sites than surveys in the 1990s. Abundances of T. eungellensis at these sites were typically low, however, and well below abundance levels prior to declines in the mid-1980s. As with surveys in the 1990s, T. eungellensis was scarce at high-elevation sites above 600 metres altitude. Numbers of this species do not appear to have increased significantly since the mid-1990s, suggesting recovery of T. eungellensis populations is occurring slowly, at best. In contrast with T. eungellensis, T. liemi was frequently recorded at high-elevation sites, albeit at low densities. As with previous surveys, surveys during 2000–2015 were unsuccessful in locating R. vitellinus. Further frog surveys and monitoring (including disease surveillance) are needed to better assess the status of stream frogs at Eungella, and to understand the influence of Bd on the abundance and distribution of threatened stream-dwelling frogs at Eungella

Chiral symmetry restoration and axial vector renormalization for Wilson fermions

Lattice gauge theories with Wilson fermions break chiral symmetry. In the U(1) axial vector current this manifests itself in the anomaly. On the other hand it is generally expected that the axial vector flavour mixing current is non-anomalous. We give a short, but strict proof of this to all orders of perturbation theory, and show that chiral symmetry restauration implies a unique multiplicative renormalization constant for the current. This constant is determined entirely from an irrelevant operator in the Ward identity. The basic ingredients going into the proof are the lattice Ward identity, charge conjugation symmetry and the power counting theorem. We compute the renormalization constant to one loop order. It is largely independent of the particular lattice realization of the current.Comment: 11 pages, Latex2

Transport Properties of the Quark-Gluon Plasma -- A Lattice QCD Perspective

Transport properties of a thermal medium determine how its conserved charge densities (for instance the electric charge, energy or momentum) evolve as a function of time and eventually relax back to their equilibrium values. Here the transport properties of the quark-gluon plasma are reviewed from a theoretical perspective. The latter play a key role in the description of heavy-ion collisions, and are an important ingredient in constraining particle production processes in the early universe. We place particular emphasis on lattice QCD calculations of conserved current correlators. These Euclidean correlators are related by an integral transform to spectral functions, whose small-frequency form determines the transport properties via Kubo formulae. The universal hydrodynamic predictions for the small-frequency pole structure of spectral functions are summarized. The viability of a quasiparticle description implies the presence of additional characteristic features in the spectral functions. These features are in stark contrast with the functional form that is found in strongly coupled plasmas via the gauge/gravity duality. A central goal is therefore to determine which of these dynamical regimes the quark-gluon plasma is qualitatively closer to as a function of temperature. We review the analysis of lattice correlators in relation to transport properties, and tentatively estimate what computational effort is required to make decisive progress in this field.Comment: 54 pages, 37 figures, review written for EPJA and APPN; one parag. added end of section 3.4, and one at the end of section 3.2.2; some Refs. added, and some other minor change