この講義では0+1次元と1+1次元における場の量子論とその対称性の量子異常(量子アノマリー、’t Hooft anomaly)を扱う。特に、対称性の状態空間(ヒルベルト空間)への作用と量子異常の関係に焦点を当てたい。
講義の前半では0+1次元場の理論、つまり量子力学について、まず対称性を取り扱うための基本となるWignerの定理を紹介する。
Wignerの定理においては一般に量子力学の状態空間は対称性群の元で射影表現をなすが、この射影因子が量子力学系のダイナミクスを拘束する例を見る。また、量子力学における対称性の射影因子と1+1次元の対称性保護トポロジカル相の関係をみる。
後半では1+1次元の場の理論において、射影表現の類似物が場の量子論を線分上で境界条件付きで量子化することにより得られることを見て、U(1)の場合にこれが量子異常のよりconventionalな定義と一致することを見る。
時間が許せば1+1次元の$Z_2$対称性の量子異常の繰り込み群流れへの応用(CP1模型)を紹介したい。
講義ノートは https://kantohm11.github.io/symmetry_review/ において公開される。(現在準備中で、順次更新する。)

We construct an effective field theory of a two-neutron halo nucleus in the limit where the two-neutron separation energy and the neutron-neutron two-body virtual energy are smaller than any other energy scale in the problem, but the scattering between the core and a single neutron is not fine-tuned, and the Efimov effect does not operate. The theory has one dimensionless coupling, which formally runs to a Landau pole in the ultraviolet. I will demonstrate some universal properties of the system, such as the ratio of the mean-square matter radius and charge radius and the shape of the E1 dipole strength function. I will also discuss the application of our EFT to 22C nucleus, where higher-order corrections to our theory are estimated as of order 20% or less if the two-neutron separation energy is less than 100 keV and the s-wave scattering length between a neutron and a 20C nucleus is less than 2.8 fm.

[Ref]
– M. Hongo, D. T. Son, arXiv:2201.09912 [nucl-th]

In this talk, chiral symmetry breaking and condensation in large N QCD are shown by utilizing Ward-Takahashi identity and QCD inequality. I will also show some comparisons with discussions in Coleman-Witten [PRL45(1980)100] and Veneziano [PLB95(1980)90].

The complex Langevin method (CLM) is one of the promising approaches to overcome the sign problem in conventional Monte Carlo simulations and is expected to reveal the phase diagram of QCD in the high-density region. On the other hand, the CLM is reliable only when the probability distribution of the drift term falls off exponentially or faster. Whether the CLM is reliable or not in the high-density region is still an open problem. In this talk, I will present recent results on the physics of QCD at finite density, based on the reliability of the CLM. I will also discuss possible setups to realize color superconductivity for future CLM simulations.

In this talk, we make a close comparison of a covariant definition of an energy/entropy in general relativity, recently proposed by a collaboration including the present authors, with existing definitions of energies such as the one from the pseudo-tensor and the quasi-local energy. We show that existing definitions of energies in general relativity are conserved charges from the Noether’s 2nd theorem for the general coordinate transformation, whose conservations are merely identities implied by the local symmetry and always hold without using equations of motion. Thus none of existing definitions in general relativity reflects the dynamical properties of the system, need for a physical definition of an energy. In contrast, our new definition of the energy/entropy in general relativity is generically a conserved non-Noether charge and gives physically sensible results for various cases such as the black hole mass, the gravitational collapse, and the expanding universe, while existing definitions sometimes lead to unphysical ones including zero and infinity. We conclude that our proposal is more physical than existing definitions of energies. Our proposal makes it possible to define almost uniquely the covariant and conserved energy/entropy in general relativity, which brings some implications to future investigations.

In this talk, I will introduce the techniques of radio polarimetry and Faraday rotation for the study of cosmic magnetic fields. Faraday rotation is a birefringent effect caused by magnetised plasma along the line of sight, which we measure using the frequency-dependent rotation of the plane of linearly polarized light from radio galaxies (i.e. synchrotron emission). Radio galaxies can be observed throughout the majority of the history of the Universe and are thus excellent beacons for measuring the properties of the cosmic web and their evolution with cosmic time. In particular, I will highlight recent results from the Low Frequency Array (LOFAR) radio telescope. LOFAR is the world’s premier low-frequency radio telescope, providing exceptional RM precision, in addition to unrivalled angular resolution, sensitivity and image fidelity, which facilitates the reliable identification of the host galaxy through comparison with optical and infrared data (from which one can then determine the redshift). Our recent work shows how these capabilities are allowing us to transform our understanding of cosmic magnetic fields and are providing a new way to study the properties of filaments and voids of the cosmic web in general.

We study SU(N) gauge fields that couple to the inflaton through the Chern-Simons term. In this talk, I will shortly review the dynamics of SU(2) gauge fields during inflation and provide a general procedure to construct homogeneous, isotropic, and attractor solutions of SU(N) gauge fields during inflation. As specific examples, we construct the stable solutions for N=3 and 4 and numerically confirm that they are complete and attractor. I will also discuss the linear perturbations in our model. It is straightforward to apply our procedure to the other simple Lie groups.

Confinement of 4d gauge theories is usually the strong-coupling problem, and we would like to develop its semiclassical understanding based on the idea of volume independence, or adiabatic continuity. We conjecture that the strong-coupling regime of many 4d gauge theories is continuously connected to the weak-coupling theories on $¥mathbb{R}^2¥times T^2$ on small $T^2$ with the nontrivial ‘t Hooft flux. We explicitly confirm the fractional theta periodicity for pure YM and chiral Lagrangian for QCD can be derived in this small $T^2$ regime. We also uncover why this is possible in view of anomaly-preservation of this compactification.

Electroweak baryogenesis is a promising scenario to explain the origin of the baryon asymmetry of the Universe. In order to realize the scenario, the electroweak phase transition should be strongly first order. The sphaleron decoupling condition is the criterion for the strongly first-order electroweak phase transition. In this talk, we discuss the sphaleron decoupling condition in extended Higgs models. We show that upper bounds on masses of additional Higgs bosons can be obtained by utilizing the sphaleron decoupling condition and the unitarity bound. This talk is based on the papers [arXiv: 2005.05250, 2201.04791].

IKKT matrix model, proposed as a non-perturbative formulation of type IIB superstring theory, has a rich structure even at a classical level. While the degrees of freedom of strings are considered to be implemented in the matrices of the theory, their exact interpretation has not been fully understood yet. In this talk, I will review the interpretation of the matrices in which the gravitational degrees of freedom appear as vielbeins of the Weitzenboeck connection in a nearly commutative limit (so called the semi-classical limit). In the interpretation, Einstein’s equations appear as a one-loop effect while the classical equations of motion of the matrix model can be interpreted as “pre-gravity.” I will explain the pre-gravity theory and show its gravitational solutions.