Fluctuations in the vicinity of the phase transition line for two flavor QCD

We study the susceptibilities of quark number, isospin number and electric charge in numerical simulations of lattice QCD at high temperature and density. We discuss the equation of state for 2 flavor QCD at non-zero temperature and density. Derivatives of $\ln Z$ with respect to quark chemical potential $(\mu_q)$ are calculated up to sixth order. From this Taylor series, the susceptibilities are estimated as functions of temperature and $\mu_q$. Moreover, we comment on the hadron resonance gas model, which explains well our simulation results below $T_c$.Comment: 3 pages, 5 figures, Talk presented at Lattice2004(non-zero

The QCD phase transition at high temperature and low density

We study the thermal properties of QCD in the presence of a small quark chemical potential $\mu$. Derivatives of the phase transition point with respect to $\mu$ are computed at $\mu=0$ for 2 and 3 flavors of p-4 improved staggered fermions on a $16^3\times4$ lattice. Moreover we contrast the case of isoscalar and isovector chemical potentials, quantify the effect of $\mu\not=0$ on the equation of state, and comment on the screening effect by dynamical quarks and the complex phase of the fermion determinant in QCD with $\mu\not=0$.Comment: Lattice2002(nonzerot), 3 pages, 2 figure

QCD at non-zero temperature and density from the lattice

The study of systems as diverse as the cores of neutron stars and heavy-ion collision experiments requires the understanding of the phase structure of QCD at non-zero temperature, T, and chemical potential, mu_q. We review some of the difficulties of performing lattice simulations of QCD with non-zero mu_q, and outline the re-weighting method used to overcome this problem. This method is used to determine the critical endpoint of QCD in the (mu_q,T) plane. We study the pressure and quark number susceptibility at small mu_q.Comment: 5 pages, talk presented by C.R. Allton at the QCD Downunder Conference, Barossa Valley and Adelaide, March 200

The QCD thermal phase transition in the presence of a small chemical potential

We propose a new method to investigate the thermal properties of QCD with a small quark chemical potential $\mu$. Derivatives of the phase transition point with respect to $\mu$ are computed at $\mu=0$ for 2 flavors of p-4 improved staggered fermions with $ma=0.1,0.2$ on a $16^3\times4$ lattice. The resulting Taylor expansion is well behaved for the small values of $\mu_{\rm q}/T_c\sim0.1$ relevant for RHIC phenomenology, and predicts a critical curve $T_c(\mu)$ in reasonable agreement with estimates obtained using exact reweighting. In addition, we contrast the case of isoscalar and isovector chemical potentials, quantify the effect of $\mu\not=0$ on the equation of state, and comment on the complex phase of the fermion determinant in QCD with $\mu\not=0$.Comment: 26 pages, 25 figures, minor modificatio

The (LATTICE) QCD Potential and Running Coupling: How to Accurately Interpolate between Multi-Loop QCD and the String Picture

We present a simple parameterization of a running coupling constant, defined via the static potential, that interpolates between 2-loop QCD in the UV and the string prediction in the IR. Besides the usual \Lam-parameter and the string tension, the coupling depends on one dimensionless parameter, determining how fast the crossover from UV to IR behavior occurs (in principle we know how to take into account any number of loops by adding more parameters). Using a new Ansatz for the LATTICE potential in terms of the continuum coupling, we can fit quenched and unquenched Monte Carlo results for the potential down to ONE lattice spacing, and at the same time extract the running coupling to high precision. We compare our Ansatz with 1-loop results for the lattice potential, and use the coupling from our fits to quantitatively check the accuracy of 2-loop evolution, compare with the Lepage-Mackenzie estimate of the coupling extracted from the plaquette, and determine Sommer's scale $r_0$ much more accurately than previously possible. For pure SU(3) we find that the coupling scales on the percent level for $\beta\geq 6$.Comment: 47 pages, incl. 4 figures in LaTeX [Added remarks on correlated vs. uncorrelated fits in sect. 4; corrected misprints; updated references.

Activity recognition using a supervised non-parametric hierarchical HMM

The problem of classifying human activities occurring in depth image sequences is addressed. The 3D joint positions of a human skeleton and the local depth image pattern around these joint positions define the features. A two level hierarchical Hidden Markov Model (H-HMM), with independent Markov chains for the joint positions and depth image pattern, is used to model the features. The states corresponding to the H-HMM bottom level characterize the granular poses while the top level characterizes the coarser actions associated with the activities. Further, the H-HMM is based on a Hierarchical Dirichlet Process (HDP), and is fully non-parametric with the number of pose and action states inferred automatically from data. This is a significant advantage over classical HMM and its extensions. In order to perform classification, the relationships between the actions and the activity labels are captured using multinomial logistic regression. The proposed inference procedure ensures alignment of actions from activities with similar labels. Our construction enables information sharing, allows incorporation of unlabelled examples and provides a flexible factorized representation to include multiple data channels. Experiments with multiple real world datasets show the efficacy of our classification approach

Single impurity operators at critical wrapping order in the beta-deformed N=4 SYM

We study the spectrum of one single magnon in the superconformal beta-deformed N=4 SYM theory in the planar limit. We compute the anomalous dimensions of one-impurity operators O_{1,L}= tr(phi Z^{L-1}), including wrapping contributions at their critical order L.Comment: LaTeX, feynmf, Metapost, 20 pages, 11 figures, v2: results up to 11 loops completed, appendix on integral calculation extende

Evidence for SU(3) symmetry breaking from hyperon production

We examine the SU(3) symmetry breaking in hyperon semileptonic decays (HSD) by considering two typical sets of quark contributions to the spin content of the octet baryons: Set-1 with SU(3) flavor symmetry and Set-2 with SU(3) flavor symmetry breaking in HSD. The quark distributions of the octet baryons are calculated with a successful statistical model. Using an approximate relation between the quark fragmentation functions and the quark distributions, we predict polarizations of the octet baryons produced in $e^+e^-$ annihilation and semi-inclusive deeply lepton-nucleon scattering in order to reveal the SU(3) symmetry breaking effect on the spin structure of the octet baryons. We find that the SU(3) symmetry breaking significantly affects the hyperon polarization. The available experimental data on the $\Lambda$ polarization seem to favor the theoretical predictions with SU(3) symmetry breaking. We conclude that there is a possibility to get a collateral evidence for SU(3) symmetry breaking from hyperon production. The theoretical errors for our predictions are discussed.Comment: 3 tables, 14 figure

The dynamics of quark-gluon plasma and AdS/CFT

In these pedagogical lectures, we present the techniques of the AdS/CFT correspondence which can be applied to the study of real time dynamics of a strongly coupled plasma system. These methods are based on solving gravitational Einstein's equations on the string/gravity side of the AdS/CFT correspondence. We illustrate these techniques with applications to the boost-invariant expansion of a plasma system. We emphasize the common underlying AdS/CFT description both in the large proper time regime where hydrodynamic dynamics dominates, and in the small proper time regime where the dynamics is far from equilibrium. These AdS/CFT methods provide a fascinating arena interrelating General Relativity phenomenae with strongly coupled gauge theory physics.Comment: 35 pages, 3 figures. Lectures at the 5th Aegean summer school, `From gravity to thermal gauge theories: the AdS/CFT correspondence'. To appear in the proceedings in `Lecture Notes in Physics

Moments of Nucleon Light Cone Quark Distributions Calculated in Full Lattice QCD

Moments of the quark density, helicity, and transversity distributions are calculated in unquenched lattice QCD. Calculations of proton matrix elements of operators corresponding to these moments through the operator product expansion have been performed on $16^3 \times 32$ lattices for Wilson fermions at $\beta = 5.6$ using configurations from the SESAM collaboration and at $\beta = 5.5$ using configurations from SCRI. One-loop perturbative renormalization corrections are included. At quark masses accessible in present calculations, there is no statistically significant difference between quenched and full QCD results, indicating that the contributions of quark-antiquark excitations from the Dirac Sea are small. Close agreement between calculations with cooled configurations containing essentially only instantons and the full gluon configurations indicates that quark zero modes associated with instantons play a dominant role. Naive linear extrapolation of the full QCD calculation to the physical pion mass yields results inconsistent with experiment. Extrapolation to the chiral limit including the physics of the pion cloud can resolve this discrepancy and the requirements for a definitive chiral extrapolation are described.Comment: 53 Pages Revtex, 26 Figures, 9 Tables. Added additional reference and updated referenced data in Table I