Preserving the symmetries of massless fermions is a well-known challenge in lattice field theory. I’ll discuss symmetry-preserving lattice regularizations of 2d QED with one and two flavors of Dirac fermions, as well as the `3450′ chiral gauge theory. The construction leverages bosonization and recently-proposed modifications of Villain-type lattice actions. The internal global symmetries act just as locally on the lattice as they do in the continuum, the anomalies are reproduced at finite lattice spacing, and in each case we’ve found a sign-problem-free dual formulation.

https://www-conf.kek.jp/kincha/

Axial gauge has been used in many perturbative calculations. However, it sometimes leads to puzzling results. In this talk, I will discuss a specific example in the context of heavy quark and quarkonium transport coefficients, where naive application of temporal axial gauge leads to an incorrect result. Then I will discuss the origin of the problem from both perturbative and nonperturbative aspects. Finally I will summarize the applicability condition of axial gauge and give a few examples.

We study a mechanism of generating the trispectrum (4-point correlation) of curvature perturbation through the dynamics of a spectator axion field and U(1) gauge field during inflation. Owing to the Chern-Simons coupling, only one helicity mode of the gauge field experiences a tachyonic instability and sources scalar perturbations. Sourced curvature perturbation exhibits parity-violating nature which can be tested through its trispectrum. We numerically compute the parity-even and parity-odd components of the sourced trispectrum. It is found that the ratio of parity-odd to parity-even mode can reach O(10%) in an exact equilateral momentum configuration. We also investigate a quasi-equilateral shape where only one of the momenta is slightly longer than the other three, and find that the parity-odd mode can reach, and more interestingly, surpass the parity-even one. This may help us to interpret a large parity-odd trispectrum signal extracted from BOSS galaxy-clustering data.