Among the most ubiquitous phases of matter, gases and crystalline solids are definitely the simplest to be described. Their physics is indeed almost entirely textbooks material and it can be summarized within the elegant frameworks of kinetic theory and Debye theory. Liquids and specially viscoelastic systems and amorphous materials (e.g. glasses) exhibit a much richer and complex dynamics with provides a large set of fundamental and unresolved physical questions. Given the tremendous microscopic complexity of these systems, which is manifest in a large landscape of scales and anomalous behaviours, the effective field theory (EFT) paradigm of isolating only a few, but fundamental, information could provide a winning approach. This talk is based on the simple, but indeed extremely difficult, question of whether these phases of matter can be distinguished, classified and understood using emergent and/or fundamental symmetry principles as in their ordered crystal counterpart. More precisely, we will combine EFTs, hydrodynamics and holographic methods to tackle the above question. I will present the most recent developments in this direction and I will discuss with you the most important open questions and avenues to explore in the near future.

Einstein gravity is not renormalizable and does not hold perturbative unitarity at high energy. This is the main reason why the construction of quantum gravity is difficult. A conjecture was proposed by Llewellyn Smith, "renormalizablility and tree-unitarity at high energy give the same conditions for theories". This conjecture would be important because it shows that, if a theory is constructed s.t. unitarity is satisfied, renormalizablility holds automatically, and vice versa.
Unfortunately, a counterexample was pointed out. If a theory involves higher derivatives, there exists a theory which is renormalizable but does not satisfy tree-unitarity. A candidate of quantum gravity, the quadratic gravity (R_{\mu\nu}^2 gravity), is one of the examples. Therefore, Llewellyn Smith's conjecture would not be useful for the discussion of quantum gravity. Then, we introduce a new conjecture, "renormalizablility and S-matrix unitarity (or often called pseudo-unitarity) at high energy give the same conditions for theories".
In this talk, Llewellyn Smith's conjecture and our contribution to it will be explained. Then, our new conjecture will be introduced. Finally, it will be shown that our conjecture works well even in theories with higher derivatives.

High-harmonic generation (HHG) is an intriguing nonlinear phenomenon induced by a strong electric field. It has been originally observed and studied in atomic and molecular gases, and is used in attosecond laser sources as well as spectroscopies. An observation of HHG in semiconductors expanded the scope of this field to condensed matters [1]. The HHG in condensed matters is attracting interests since it may be used as new laser sources and/or as powerful tools to detect band information such as the Berry curvatures. Recently, further exploration of the HHG in condensed matters are carried out in various other systems than semiconductors.

In this talk, we introduce our recent theoretical efforts on the HHG in strongly correlated systems [2,3,4]. In contract to semiconductors, the charge carriers are not normal fermions, which makes HHG in strongly correlated systems unclear. Using the dynamical-mean field theory and the infinite time-evolving block decimation for the Hubbard model, we reveal the HHG features in the Mott insulators. Firstly, we reveal that the origin of the HHG in the Mott insulator is the recombination of doublons (doubly occupied sites) and holons (no electron site). Then, we show that the HHG feature qualitatively changes depending on the field strength due to the change of mobility of charge carriers, and discuss that the HHG directly reflects the dynamics of many body elemental excitations, which the single particle spectrum may miss. These results indicate that the HHG in Mott systems may be used as a spectroscopic tool for many body excitations. We also discuss the effects of spin dynamics on the HHG, which is a unique feature in strongly correlated systems.

The Cosmic Microwave Background (CMB) gives a photographic image of the Universe when it was still an “infant”. We have been using it to test our ideas about the origin of the Universe. The CMB research told us a remarkable story: the structure we see in our Universe such as galaxies, stars, planets, and eventually ourselves originated from tiny quantum fluctuations in the period of the early Universe called cosmic inflation. While we have accumulated strong evidence for this picture, the extraordinary claim requires extraordinary evidence. The last prediction of inflation that is yet to be confirmed is the existence of primordial gravitational waves whose wavelength can be as big as billions of light years. To this end we have proposed to JAXA a new satellite mission called LiteBIRD, whose primary scientific goal is to find signatures of gravitational waves in the polarisation of the CMB. In this presentation we describe physics of gravitational waves from inflation, and the LiteBIRD proposal.