The transverse structure of the QCD string

The characterization of the transverse structure of the QCD string is discussed. We formulate a conjecture as to how the stress-energy tensor of the underlying gauge theory couples to the string degrees of freedom. A consequence of the conjecture is that the energy density and the longitudinal-stress operators measure the distribution of the transverse position of the string, to leading order in the string fluctuations, whereas the transverse-stress operator does not. We interpret recent numerical measurements of the transverse size of the confining string and show that the difference of the energy and longitudinal-stress operators is the appropriate probe to use when comparing with the next-to-leading order string prediction. Secondly we derive the constraints imposed by open-closed string duality on the transverse structure of the string. We show that a total of three independent `gravitational' form factors characterize the transverse profile of the closed string, and obtain the interpretation of recent effective string theory calculations: the square radius of a closed string of length \beta, defined from the slope of its gravitational form factor, is given by (d-1)/(2\pi\sigma)\log(\beta/(4r_0)) in d space dimensions. This is to be compared with the well-known result that the width of the open-string at mid-point grows as (d-1)/(2\pi\sigma) log(r/r_0). We also obtain predictions for transition form factors among closed-string states.Comment: 21 pages, 1 figur

Unifying Requirements and Code: an Example

Requirements and code, in conventional software engineering wisdom, belong to entirely different worlds. Is it possible to unify these two worlds? A unified framework could help make software easier to change and reuse. To explore the feasibility of such an approach, the case study reported here takes a classic example from the requirements engineering literature and describes it using a programming language framework to express both domain and machine properties. The paper describes the solution, discusses its benefits and limitations, and assesses its scalability.Comment: 13 pages; 7 figures; to appear in Ershov Informatics Conference, PSI, Kazan, Russia (LNCS), 201

Lattice Gauge Theory Sum Rule for the Shear Channel

An exact expression is derived for the $(\omega,p)=0$ thermal correlator of shear stress in SU($N_c$) lattice gauge theory. I remove a logarithmic divergence by taking a suitable linear combination of the shear correlator and the correlator of the energy density. The operator product expansion shows that the same linear combination has a finite limit when $\omega\to\infty$. It follows that the vacuum-subtracted shear spectral function vanishes at large frequencies at least as fast as $\alpha_s^2(\omega)$ and obeys a sum rule. The trace anomaly makes a potential contribution to the spectral sum rule which remains to be fully calculated, but which I estimate to be numerically small for $T\gtrsim 3T_c$. By contrast with the bulk channel, the shear channel spectral density is then overall enhanced as compared to the spectral density in vacuo.Comment: 11 pages, no figure

Density, short-range order and the quark-gluon plasma

We study the thermal part of the energy density spatial correlator in the quark-gluon plasma. We describe its qualitative form at high temperatures. We then calculate it out to distances approx. 1.5/T in SU(3) gauge theory lattice simulations for the range of temperatures 0.9<= T/T_c<= 2.2. The vacuum-subtracted correlator exhibits non-monotonic behavior, and is almost conformal by 2T_c. Its broad maximum at r approx. 0.6/T suggests a dense medium with only weak short-range order, similar to a non-relativistic fluid near the liquid-gas phase transition, where eta/s is minimal.Comment: 4 pages, 4 figure

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

QCD at non-zero temperature from the lattice

I review the status of lattice QCD calculations at non-zero temperature. After summarizing what is known about the equilibrium properties of strongly interacting matter, I discuss in more detail recent results concerning the quark-mass dependence of the thermal phase transition and the status of calculations of non-equilibrium properties.Comment: 20 pages, 2 figures, proceedings of the Lattice 2015 conference in Kobe, Japa