It has been a long-standing problem to analytically prove confinement of pure Yang-Mills theory. One possible scenario is to start with the weakly-coupled region, obtain the trans-series expansion with respect to gauge coupling constant, and then continue back to the strongly-coupled region, with the help of mathematics of “resurgence”. The program has been pursued mostly on the geometry R^3 x S^1, however there the trans-series expansion could be spoiled by IR divergences. In this talk we discuss 4d SU(N) Yang-Mills theory on R×T^3, with twisted boundary condition eliminating IR zero modes. By connecting the 4d Yang-Mills theory to 2d CP^{N-1}-model, we find that the fractional instantons connecting N vacua of the CP^{N-1}-model dynamically restores center symmetry. This talk is based on arXiv:1704.05852, in collaboration with Kazuya Yonekura.

Thanks to the successful operations of Fermi-LAT and MAGIC telescopes, the emission mechanism of gamma-ray pulsars has been getting clearer in the last 10 years. The number of detecter pulsars has increased from less than 10 to more than 200, and those emission can be basically explained as the Curvature radiation from the Outer Gap. On the other hand, new problems have also been found. For example, very high energy emission from the Crab pulsar could not be explained by the Curvature radiation. In this seminar, I will talk about the basic models of gamma-ray pulsar and observational and theoretical progress in the last 10 years, together with the future prospect of CTA observations.

If the neutrino mass ordering turns out to be inverted, one may always reorder it to be normal. In this case the resulting pattern of the PMNS matrix looks strange and needs an explanation. Given the normal neutrino mass ordering, on the other hand, one is usually concerned about how small the effective Majorana mass term of a neutrinoless double-beta decay can be. In this seminar I will address both issues by presenting some new phenomenological observations, and discuss a possible connection between the mu-tau reflection symmetry breaking and the neutrino mass ordering, octant of theta(23) and CP violation.

量子アニーリングは、量子効果を利用して組み合わせ最適化問題(＝複雑な相互作用を持つイジング模型の基底状態探索）を解くための枠組みである。本講演では、その基本的な考え方と定式化やハードウェアでの実装状況を説明するとともに，最近急速に研究が活性化しているnon-stoquasticハミルトニアンの問題について解説する。

Weak values were introduced as outcomes of weak measurements performed on ensembles of pre- and post-selected quantum systems, i.e., a conditional expectation value. I will argue that a weak value of an observable is a robust property of a single pre- and post-selected quantum system rather than a statistical property. During an infinitesimal time a system with a given weak value affected other systems as if it had been in an eigenstate with eigenvalue equal to the weak value. The difference between the weak value and the expectation value has been demonstrated experimentally on the example of photon polarization

We discuss the sign problem based on our recent two papers [1,2].
The sign problem is one of the grand challenges in theoretical physics, and it is also a problem relevant to recent heavy-ion collision experiments. In heavy-ion collisions at colliding eneriges of $¥sqrt{s_{NN}}=5-20$ GeV, recent data seem to suggest the existence of the first order QCD phase transition, while the existence of massive neutron stars implies that the EOS of dense matter needs to be stiff enough. It is desired to obtain the QCD phase boundary and EOS in the first-principles method, Monte Carlo simulations of lattice QCD, but the sign problem in finite density QCD prevents us to obtain precise results.
Recently developed two methods, the complex Langevin method (CLM) and the Lefschetz thimble method (LTM), are promising. In these methods, real variables are extended to complex, integration path/regions are modified from the original path, and can solve or at least circumvent the sign problem. Still, we have problems when singular points are located near the original integration path.
In the first part, we discuss the Lefschetz thimbles in the NJL model with vector interaction [1].
The NJL model has been utilized to discuss the QCD phase diagram, but it is not easy to apply CLM and LTM. Even in the mean field treatment of the NJL model, we have many singular points coming from the fermion determinant. Furthermore, when we introduce the vector interaction, another sign problem arises from the Wick rotation of the temporal component of the auxiliary vector field (auxiliary sign problem). We have found that these two problems can be in principle solved in LTM.
It is possible to obtain thimbles by requiring that the momentum integration path is chosen to be on the same Riemann sheet along the flow trajectories.
The latter problem can be handled by complexifying the vector field. In practice, however, the flow trajectories stop after some time near the fixed points.
In the second part, we propose a new method, the path optimization method (POM), to search for the integration path [2].
Since the flow equation in LTM blows up at some point in most of the actions, it is favorable to obtain the new integration path without solving the flow equation. One of the natural ideas is to apply the variational method. We first give the trial function which parametrize the integration path, and optimize the trial function by minimizing the weight cancellation (or by minimizing the cost function). We apply POM to a gaussian model [3]. We have found that the optimized path agrees with the thimbles around the fixed points, the local maxima of the Boltzmann weights, and the analytic results are well reproduced even in the parameter region where the sign problem is very severe and CLM is found to fail. Thus POM seems to be another promising tool for the sign problem. In the presentation, we also show some more recent results of POM.
[1] Lefschetz thimbles in fermionic effective models with repulsive vector-field, Yuto Mori, Kouji Kashiwa, Akira Ohnishi, arXiv:1705.03646 [hep-lat].
[2] Toward solving the sign problem with path optimization method, Yuto Mori, Kouji Kashiwa, Akira Ohnishi, arXiv:1705.05605 [hep-lat].
[3] New Insights into the Problem with a Singular Drift Term in the Complex Langevin Method, J. Nishimura and S. Shimasaki, Phys. Rev. D92, 011501 (2015), arXiv:1504.08359.

The standard paradigm of collisionless cold dark matter is in tension with measurements on large scales. In particular, the best fit values of the Hubble rate H0 and the matter density perturbation sigma8 inferred from the cosmic microwave background seem inconsistent with the results from direct measurements. We show that both problems can be solved in a framework in which dark matter consists of two distinct components, a dominant component and a subdominant component. The primary component is cold and collisionless. The secondary component is also cold, but interacts strongly with dark radiation, which itself forms a tightly coupled fluid. The growth of density perturbations in the subdominant component is inhibited by dark acoustic oscillations due to its coupling to the dark radiation, solving the σ8 problem, while the presence of tightly coupled dark radiation ameliorates the H0 problem. The subdominant component of dark matter and dark radiation continue to remain in thermal equilibrium until late times, inhibiting the formation of a dark disk. We present an example of a simple model that naturally realizes this scenario in which both constituents of dark matter are thermal WIMPs. Our scenario can be tested by future stage-IV experiments designed to probe the CMB and large scale structure.

最近、カイラルゲージ理論の非摂動的な定式化としてdomain-wall fermionとgradient flowを組み合わせた方法がKaplanたちにより提案された。通常のdomain-wall fermionでは2枚のdomain wall上にそれぞれ異なるカイラリティを持った無質量フェルミオンが局在するが、ここでバルクのゲージ場をgradient flowを用いて減衰させることで、片方のカイラリティのフェルミオンのみがゲージ場と相互作用できるようになる。我々はこの方法をもとに、4次元のベクトル的な理論における軸性U(1)カレントについて調べた。軸性U(1)カレントの素朴な定義として、gradient flowで減衰していく仮想的なU(1)ゲージ場を新たに導入し、そのU(1)ゲージ場のdomain wall上の値で有効作用を変分したものを考えた。しかし、このカレントはバルクの寄与も含んでおり保存してしまいアノマリーを再現しないことがわかった。本講演ではまずKaplanたちの定式化を簡単に紹介した後、この軸性U(1)カレントの保存について解説する。最後に、正しくアノマリーを再現するような軸性U(1)カレントの定義を提案する。

We discuss generalization of the Nambu-Goldstone theorem to open classical and quantum systems. For a Hamiltonian system, it is known that there appears a gapless excitation called the Nambu-Goldstone mode, when a global continuum symmetry is spontaneously broken. In this theorem, a conservation law plays an important role. In contrast, for an open system, the ordinary conservation law is violated because of interaction with environment. Nevertheless, we can define another symmetry using path integral formalism, whose Noether charge is different from ordinary one. We show that the Nambu-Goldstone mode appears when the symmetry is spontaneously broken in the open system. The NG mode is generally not propagating but dissipative. We also show the general form of the dispersion relation using Ward-Takahashi identity.  We discuss application to a real system such as an active matter system.

We study correlation functions in a scalar field theory on the fuzzy sphere, which is realized by a matrix model where the matrix size plays a role of the UV cutoff. We identify the Berezin symbol for a matrix with a field, and we calculate the correlation functions of the fields by Monte Carlo simulation. By tuning a parameter of the theory, we find that the two-point and four-point correlation functions agree for different matrix sizes. This result strongly suggests that the theory is renormalizable.