_{L}⨯U(1) intact, with the Higgs potential being generated at the loop level by the coupling to the SM sector. There are also some models of this type being actively investigated.

The next plenary speaker was Stefano Forte, who reviewed the status and prospects of determining the strong coupling α

_{s}from sources other than the lattice. The PDG average for α

_{s}is a weighted average of six values, four of which are the pre-averages of the determinations from the lattice, from τ decays, from jet rates and shapes, and from parton distribution functions, and two of which are the determinations from the global electroweak fit and from top production at the LHC. Each of these channels has its own systematic issues, and one problem can be that overaggressive error estimates give too much weight to the corresponding determination, leading to statistically implausible scatter of results in some channels. It should be noted, however, that the lattice results are all quite compatible, with the most precise results by ALPHA and by HPQCD (which use different lattice formulations and completely different analysis methods) sitting right on top of each other.

This was followed by a presentation by Thomas Korzec of the determination of α

_{s}by the ALPHA collaboration. I cannot really attempt to do justice to this work in a blog post, so I encourage you to look at their paper. By making use of both the Schrödinger functional and the gradient flow coupling in finite volume, they are able to non-perturbatively run α

_{s}between hadronic and perturbative scales with high accuracy.

After the coffee break, Erhard Seiler reviewed the status of the complex Langevin method, which is one of the leading methods for simulating actions with a sign problem, e.g. at finite chemical potential or with a θ term. Unfortunately, it is known that the complex Langevin method can sometimes converge to wrong results, and this can be traced to the violation by the complexification of the conditions under which the (real) Langevin method is justified, of which the development of zeros in e

^{-S}seems to be the most important case, giving rise to poles in the force which will violate ergodicity. There seems to be a lack of general theorems for situations like this, although the complex Langevin method has apparently been shown to be correct under certain difficult-to-check conditions. One of the best hopes for simulating with complex Langevin seems to be the dynamical stabilization proposed by Benjamin Jäger and collaborators.

This was followed by Paulo Bedaque discussing the prospects of solving the sign problem using the method of thimbles and related ideas. As far as I understand, thimbles are permissible integration regions in complexified configuration space on which the imaginary part of the action is constant, and which can thus be integrated over without a sign problem. A holomorphic flow that is related both to the gradient flow and the Hamiltonian flow can be constructed so as to flow from the real integration region to the thimbles, and based on this it appears to have become possible to solve some toy models with a sign problem, even going so far as to perform real-time simulations in the Keldysh-Schwinger formalism in Euclidean space (if I understood correctly).

In the afternoon, there was a final round of parallel sessions, one of which was again dedicated to the anomalous magnetic moment of the muon, this time focusing on the very difficult hadronic light-by-light contribution, for which the Mainz group has some very encouraging first results.

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