We present results for lattice QCD with staggered fermions in the limit of infinite gauge coupling, obtained from a worm-type Monte Carlo algorithm on a discrete spatial lattice but with continuous Euclidean time. This is obtained by sending both the anisotropy parameter ξ ¼ a σ =a τ and the number of time slices N τ to infinity, keeping the ratio aT ¼ ξ=N τ fixed. The obvious gain is that no continuum extrapolation N τ → ∞ has to be carried out. Moreover, the algorithm is faster, and the sign problem disappears. We derive the continuous time partition function and the corresponding Hamiltonian formulation. We compare our computations with those on discrete lattices and study both zero and finite temperature properties of lattice QCD in this regime.

Lattice QCD with staggered fermions at strong coupling has long been studied in a dual representation to circumvent the finite baryon density sign problem. Monte Carlo simulations at finite temperature and density require anisotropic lattices. Recent results that established the nonperturbative functional dependence between the bare anisotropy γ and the physical anisotropy a s /a t in the chiral limit are now extended to finite quark mass. We illustrate how the calibration of the anisotropy works and discuss the consequences of the anisotropy on thermodynamic observables. We also show first results on the energy density and pressure in the QCD phase diagram in the strong coupling regime.

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We present results for lattice QCD in the limit of infinite gauge coupling on a discrete spatial but continuous Euclidean time lattice. A worm type Monte Carlo algorithm is applied in order to sample two-point functions which gives access to the measurement of mesonic temporal correlators. The continuous time limit, based on sending N τ → ∞ and the bare anistotropy to infinity while fixing the temperature in a non-perturbative setup, has various advantages: the algorithm is sign problem free, fast, and accumulates high statistics for correlation functions. Even though the measurement of temporal correlators requires the introduction of a binning in time direction, this discretization can be chosen to be by orders finer compared to discrete computations. For different spatial volumes, temporal correlators are measured at zero spatial momentum for a variety of mesonic operators. They are fitted to extract the pole masses and corresponding particles as a function of the temperature. We conclude discussing the possibility to extract transport coefficients from these correlators.

Lattice QCD with staggered fermions can be formulated in dual variables to address the finite baryon density sign problem. In the past we have performed simulations in the strong coupling regime, including leading order gauge corrections. In order to vary the temperature for fixed β it was necessary to introduce a bare anisotropy. In this talk we will extend our work to include results from a non-perturbative determination of the physical anisotropy a σ /a τ = ξ (γ, β), which is necessary to unambiguously locate the critical end point and the first order line of the chiral transition.