Non-perturbative renormalisation of left–left four-fermion operators with Neuberger fermions

We outline a general strategy for the non-perturbative renormalisation of composite operators in discretisations based on Neuberger fermions, via a matching to results obtained with Wilson-type fermions. As an application, we consider the renormalisation of the four-quark operators entering the ΔS=1$\mathrm{\Delta }S=1$ and ΔS=2$\mathrm{\Delta }S=2$ effective Hamiltonians. Our results are an essential ingredient for the determination of the low-energy constants governing non-leptonic kaon decays.     

A quenched study of the Schrödinger functional with chirally rotated boundary conditions: Non-perturbative tuning

The use of chirally rotated boundary conditions provides a formulation of the Schrödinger functional that is compatible with automatic O(a)$\mathrm{O}(a)$ improvement of Wilson fermions up to O(a)$\mathrm{O}(a)$ boundary contributions. The elimination of bulk O(a)$\mathrm{O}(a)$ effects requires the non-perturbative tuning of the critical mass and one additional boundary counterterm. We present the results of such a tuning in a quenched setup for several values of the renormalized gauge coupling, from perturbative to non-perturbative regimes, and for a range of lattice spacings. We also check that the correct boundary conditions and symmetries are restored in the continuum limit.     

Optical helicity and Hertz vectors

We study the conserved quantity associated with the dual symmetry of the Maxwell equations, called the optical helicity, by means of transverse Hertz vectors. In the presence of charges, its evolution yields the integral of $\mathit{E}?\mathit{B}$ which is the anomaly term for chiral fermions. We also discuss the helicity change in condensed matter systems where topological magnetoelectric effect emerges. An alternative expression of the optical helicity is also found. Lastly, a dual symmetric Hertz Lagrangian is constructed and its conserved charge is derived.     

Number-theory dark matter

We propose that the stability of dark matter is ensured by a discrete subgroup of the U(1)_B–L gauge symmetry, Z₂(B–L)$Z_2(\mathrm{B}\text{–}\mathrm{L})$. We introduce a set of chiral fermions charged under the U(1)_B–L in addition to the right-handed neutrinos, and require the anomaly-cancellation conditions associated with the U(1)_B–L gauge symmetry. We find that the possible number of fermions and their charges are tightly constrained, and that non-trivial solutions appear when at least five additional chiral fermions are introduced. The Fermat theorem in the number theory plays an important role in this argument. Focusing on one of the solutions, we show that there is indeed a good candidate for dark matter, whose stability is guaranteed by Z₂(B–L)$Z_2(\mathrm{B}\text{–}\mathrm{L})$.     

A study of the sign problem for lattice QCD with chemical potential

We study the expectation value of the phase of the fermion determinant for Wilson lattice fermions with chemical potential. We use quenched SU(3)$\mathrm{SU}(3)$ ensembles and implement a recently proposed exact dimensional reduction of the fermion determinant. Ensembles at several temperatures below and above the phase transition are studied and we analyze the role of the quark mass, the temperature, the volume and the topological sectors. We compare our numerical results to predictions from chiral perturbation theory.