^{-S}real and positive. Examples include an imaginary chemical potential, an imaginary θ term, or an external electromagnetic field with a real magnetic or imaginary electric field strength. Applications include the study of the curvature of the critical line near μ=0 and the nature of the Roberge-Weiss phase transition, and the determination of electric dipole moments and the magnetic properties of nuclear matter.

Next was Tilo Wettig introducing the QPACE 2. QPACE now stands for "QCD Parallel Computing Engine" (as there is no more Cell processor involved). Each compute card consists of four Xeon Phi Knights Corner processors linked by a PCI Express bus and a weak CPU, which is only used for booting. The compute cards use a novel patented "brick" concept and employ an innovative kind of water cooling. Each rack has a peak performance of 310 TFlops. To run optimally on this architecture, codes will need some adjustments employing ideas such as site fusing, half-precision gauge fields, and the use of lattice sizes with prime factors of 3 and 5, but with optimal use of the SIMD units, scaling is almost perfect. A future successor, QPACE 3, will use Knights Landing units instead of the Knights Corner ones, and should achieve a peak performance of 1 TFlop per rack.

This was followed by Masakiyo Kitazawa speaking about measurements of thermodynamics using the gradient flow. The small-flowtime expansion for the gradient flow allows to define a renormalized energy-momentum tensor in terms of the zero-flowtime limit of two flowed dimension-four operators. This has been applied to obtain results for the trace anomaly and the entropy density, but the difficulty lies in finding a plateau region in flow time where both lattice artifacts and finite-volume effects can be neglected, so as to allow a reliable extrapolation to zero flow time.

After the coffee break, Chris Sachrajda reviewed the state of the lattice determination of long-distance effects to flavour-changing processes. As no new physics has been discovered by the LHC so far, precision flavour physics is still the most promising avenue in the search for BSM effects. For some quantities in this area, particularly in the field of Kaon physics, long distance effects are of crucial importance. An example is neutral Kaon mass difference Δm

_{K}=m

_{KL}-m

_{KS}; this involves four-volume integrals over the expectation value of matrix elements of electroweak operators between hadronic states, raising the problem of how to prepare such hadronic states in this context. The problem can be solved by taking the time integral over a largeish interval, but placing the creation and annihilation operators well outside of the corresponding four-volume. The relevant correlation functions also contain terms growing exponentially with the time extent T,

which can be removed by adding suitably tuned terms to the electroweak Hamiltonian. UV divergences are eliminated the GIM mechanism together with the V-A structure of the electroweak currents. With all these theoretical developments in place, a calculation done at unphysical pion and Kaon masses gives a result for Δm

_{K}close to the physical value (which may of course still be a fortuitous coincidence), and exhibits an apparent violation of the OZI rule in that the contribution from the disconnected diagram is very significant to the final result. Another example given was the decay K

_{L}->π

^{0}l

^{+}l

^{-}, for which the long-distance effects are known in χPT, and the question addressed by an exploratory study is whether the lattice can do better. Yet another example are the QED corrections to the pion decay constant, which contain IR divergences requiring a proper Bloch-Nordsieck treatment.

After some well-deserved applause for the organizers, the conference closed with the invitation to next year's lattice conference in Kobe, Japan, from 14th to 18th July 2014. The IAC also announced that the 2016 lattice conference will be hosted in Southampton, U.K., in the last week of July 2016.

As I had to fly back to Germany in the evening (a lecture having to be given on Monday), the posting of this and the previous day's summaries was delayed a little by travel and subsequent jetlag, but I am sure my readers will be delighted to know that I got home safe and sound, and with all my luggage intact.