Slavo Kratochvila

Observing string breaking with Wilson loops

An uncontroversial observation of adjoint string breaking is proposed, while measuring the static potential from Wilson loops only. The overlap of the Wilson loop with the broken-string state is small, but non-vanishing, so that the broken-string groundstate can be seen if the Wilson loop is long enough. We demonstrate this in the context of the (2 + 1) dS U(2) adjoint static potential, using an improved

The canonical approach to Finite Density QCD

We present a canonical approach to study properties of QCD at finite baryon density ρ, and apply it to the determination of the phase diagram of four-flavour Q CD. For a pion mass mπ ∼ 350 MeV, the first-order transition between the hadronic and the plasma phase gives rise to a coexistence region in the T -ρ plane, which we study in detail. We obtain accurate results for systems containing up to 30 baryons and quark chemical potentials μ up to 2T . Our T -μ phase diagram agrees with the literature when μ T . 1. At larger chemical potential, we observe a “bending down” of the phase boundary. We characterise the two phases with simple models: the hadron resonance gas in the hadronic phase, the free massless quark gas in the plasma phase.

QCD at zero baryon density and the Polyakov loop paradox

We compare the grand canonical partition function at fixed chemical potential µ with the canonical partition function at fixed baryon number B, formally and by numerical simulations at µ = 0 and B = 0 with four flavours of staggered quarks. We verify that the free energy densities are equal in the thermodynamic limit, and show that they can be well described by the hadron resonance gas at T Tc. Small differences between the two ensembles, for thermodynamic observables characterising the deconfinement phase transition, vanish with increasing lattice size. These differences are solely caused by contributions of non-zero baryon density sectors, which are exponentially suppressed with increasing volume. The Polyakov loop shows a different behaviour: for all temperatures and volumes, its expectation value is exactly zero in the canonical formulation, whereas it is always non-zero in the commonly used grand-canonical formulation. We clarify this paradoxical difference, and show that the non-vanishing Polyakov loop expectation value is due to contributions of non-zero triality states, which are not physical, because they give zero contribution to the partition function.

QCD at small baryon number

We consider the difficulties of finite density QCD from the canonical formalism. We present results for small baryon numbers, where the sign problem can be controlled, in particular by supplementing the μ =0 sampling with imaginary μ ensembles. We initiate the thermodynamic study of few-nucleon systems, starting with the measurement of the free energy of a few baryons in the confined and deconfined phase. We present a simple model for the phase transition, whose results are in good agreement with the literature, but extend to lower temperatures.

String breaking with Wilson loops

Abstract A convincing, uncontroversial observation of string breaking, when the static potential is extracted from Wilson loops only, is still missing. This failure can be understood if the overlap of the Wilson loop with the broken string is exponentially small. In that case, the broken string ground state will only be seen if the Wilson loop is long enough. Our preliminary results show string breaking in the context of the 3 d SU (2) adjoint static potential, using the Lu¨scher-Weisz exponential variance reduction approach. As a by-product, we measure the fundamental SU (2) static potential with improved accuracy and see clear deviations from Casimir scaling.

QCD at zero baryon density

While the grand canonical partition function Z G C (μ) with chemical potential μ explicitly breaks the Z 3 symmetry with the Dirac determinant, the canonical partition function at fixed baryon number Z C (B) is manifestly Z 3 -symmetric. We compare Z G C (μ = 0) and Z C (B = 0) formally and by numerical simulations, in particular with respect to properties of the deconfinement transition. The small differences between the two ensembles vanish with increasing lattice size. We show numerically that the free energy density is the same for both ensembles in the thermodynamic limit. As a function of the chemical potential, the pressure is close to its Stefan-Boltzmann limit for T ∼ 1.1T c already.

Testing dimensional reduction in SU(2) gauge theory

Abstract At high temperature, every ( d + 1)-dimensional theory can be reformulated as an effective theory in d dimensions. We test the numerical accuracy of this Dimensional Reduction for (3+1)-dimensional SU (2) by comparing perturbatively determined effective couplings with lattice results as the temperature is progressively lowered. We observe an increasing disagreement between numerical and perturbative values from T = 4 T c downwards.

The 3-states Potts model as a heavy quark finite density laboratory

The 3-D Z(3) Potts model is a model for finite temperature QCD with heavy quarks. The chemical potential in QCD becomes an external magnetic field in the Potts model. Following Alford et al.\cite{Alford_et_al}, we revisit this mapping, and determine the phase diagram for an arbitrary chemical potential, real or imaginary. Analytic continuation of the phase transition line between real and imaginary chemical potential can be tested with precision. Our results show that the chemical potential weakens the heavy-quark deconfinement transition in QCD.