Topological sampling through windings

We propose a modification of the Hybrid Monte Carlo (HMC) algorithm that overcomes the topological freezing of a two-dimensional U(1) gauge theory with and without fermion content. This algorithm includes reversible jumps between topological sectors – winding steps – combined with standard HMC steps. The full algorithm is referred to as winding HMC (wHMC), and it shows an improved behaviour of the autocorrelation time towards the continuum limit. We find excellent agreement between the wHMC estimates of the plaquette and topological susceptibility and the analytical predictions in the U(1) pure gauge theory, which are known even at finite $$\beta $$ β . We also study the expectation values in fixed topological sectors using both HMC and wHMC, with and without fermions. Even when topology is frozen in HMC – leading to significant deviations in topological as well as non-topological quantities – the two algorithms agree on the fixed-topology averages. Finally, we briefly compare the wHMC algorithm results to those obtained with master-field simulations of size $$L\sim 8 \times 10^3$$ L ∼ 8 × 10 3 .

Memory efficient finite volume schemes with twisted boundary conditions

In this paper we explore a finite volume renormalization scheme that combines three main ingredients: a coupling based on the gradient flow, the use of twisted boundary conditions and a particular asymmetric geometry, that for SU(N) gauge theories consists on a hypercubic box of size $$l^2 \times (Nl)^2$$ l 2 × ( N l ) 2 , a choice motivated by the study of volume independence in large N gauge theories. We argue that this scheme has several advantages that make it particularly suited for precision determinations of the strong coupling, among them translational invariance, an analytic expansion in the coupling and a reduced memory footprint with respect to standard simulations on symmetric lattices, allowing for a more efficient use of current GPU clusters. We test this scheme numerically with a determination of the $$\Lambda $$ Λ parameter in the SU(3) pure gauge theory. We show that the use of an asymmetric geometry has no significant impact in the size of scaling violations, obtaining a value $$\Lambda _{\overline{\mathrm{MS}}}\sqrt{8 t_0} =0.603(17)$$ Λ MS ¯ 8 t 0 = 0.603 ( 17 ) in good agreement with the existing literature. The role of topology freezing, that is relevant for the determination of the coupling in this particular scheme and for large N applications, is discussed in detail.

Past, present, and future of precision determinations of the QCD coupling from lattice QCD

Non-perturbative scale-dependent renormalization problems are ubiquitous in lattice QCD as they enter many relevant phenomenological applications. They require solving non-perturbatively the renormalization group equations for the QCD parameters and matrix elements of interest in order to relate their non-perturbative determinations at low energy to their high-energy counterparts needed for phenomenology. Bridging the large energy separation between the hadronic and perturbative regimes of QCD, however, is a notoriously difficult task. In this contribution we focus on the case of the QCD coupling. We critically address the common challenges that state-of-the-art lattice determinations have to face in order to be significantly improved. In addition, we review a novel strategy that has been recently put forward in order to solve this non-perturbative renormalization problem and discuss its implications for future precision determinations. The new ideas exploit the decoupling of heavy quarks to match $${N_{\mathrm{f}}}$$ N f -flavor QCD and the pure Yang–Mills theory. Through this matching the computation of the non-perturbative running of the coupling in QCD can be shifted to the computationally much easier to solve pure-gauge theory. We shall present results for the determination of the $$\varLambda $$ Λ -parameter of $${N_{\mathrm{f}}}=3$$ N f = 3 -flavor QCD where this strategy has been applied and proven successful. The results demonstrate that these techniques have the potential to unlock unprecedented precision determinations of the QCD coupling from the lattice. The ideas are moreover quite general and can be considered to solve other non-perturbative renormalization problems.

An analysis of systematic effects in finite size scaling studies using the gradient flow

We propose a new strategy for the determination of the step scaling function $$\sigma (u)$$ σ ( u ) in finite size scaling studies using the gradient flow. In this approach the determination of $$\sigma (u)$$ σ ( u ) is broken in two pieces: a change of the flow time at fixed physical size, and a change of the size of the system at fixed flow time. Using both perturbative arguments and a set of simulations in the pure gauge theory we show that this approach leads to a better control over the continuum extrapolations. Following this new proposal we determine the running coupling at high energies in the pure gauge theory and re-examine the determination of the $$\Lambda $$ Λ -parameter, with special care on the perturbative truncation uncertainties.

Polyakov loop eigenvalues in the presence of baryon chemical potential

The eigenvalues of the Polyakov loop are calculated in the strong coupled lattice QCD at finite tempera­ture. This is done both in the pure gauge theory and in the theory with heavy quarks at finite baryon chemical potential. Computations are performed in the mean­field like approach to the effective action. Using the eigenvalues obtained we also evaluate the free energy, real and imaginary parts of the Polyakov loops and the baryon density. The phase diagram of the model and influence of the baryon chemical potential are discussed in details. We underline a similarity between our calculations and continuum derivations of the phenomenon of A0 condensation.

The convolutional double copy: a case study with a point

The double copy relates scattering amplitudes in gauge and gravity theories. It has also been extended to classical solutions, and a number of approaches have been developed for doing so. One of these involves expressing fields in a variety of (super-)gravity theories in terms of convolutions of gauge fields, including also BRST ghost degrees of freedom that map neatly to their corresponding counterparts in gravity. In this paper, we spell out how to use the convolutional double copy to map gauge and gravity solutions in the manifest Lorenz and de Donder gauges respectively. We then apply this to a particular example, namely the point charge in pure gauge theory. As well as clarifying how to use the convolutional approach, our results provide an alternative point of view on a recent discussion concerning whether point charges map to the Schwarzschild solution, or the more general two-parameter JNW solution, which includes a dilaton field. We confirm the latter.

Decoupling of charm beyond leading order

We study the effective theory of decoupling of a charm quark at low energies. We do this by simulating a model, QCD with two mass-degenerate charm quarks. At leading order the effective theory is a pure gauge theory. By computing ratios of hadronic scales we have direct access to the power corrections in the effective theory. We show that these corrections follow the expected leading behavior, which is quadratic in the inverse charm quark mass.