Fermion dark matter particles can aggregate to form extended dark matter structures via a first-order phase transition in which the particles get trapped in the false vacuum. We study Fermi balls created in a phase transition induced by a generic quartic thermal effective potential. We show that for Fermi balls of mass, $10^{-7}M_{Sun} M_{¥rm FB} < 10^{-5}M _{Sun}$, correlated observations of gravitational waves produced during the phase transition (at SKA/THEIA/$¥mu$Ares), and gravitational microlensing caused by Fermi balls (at Subaru-HSC), can be made if the amount of dark radiation today is smaller than the equivalent of one neutrino. Fermi balls may collapse to primordial black holes (PBHs) if the fermion dark matter particles that comprise them interact via a sufficiently strong Yukawa force. We show that phase transitions with vacuum energy, $0.1 < B^{1/4}/{MeV} < 10^3$}, generate PBHs of mass, $10^{-20} < M_{PBH} /M_{Sun} < 10^{-16}$, and correlated isotropic extragalactic X-ray/$¥ gamma$-ray background from PBH evaporation (at AMEGO-X/e-ASTROGAM).

We clarify relations among topological solitons in various dimensions: a domain wall, non-Abelian vortex, magnetic monopole, and Yang-Mills instanton, together with a (non-Abelian) sine-Gordon soliton, baby skyrmion (lump), and skyrmion. We construct a composite configuration consisting of a domain wall, vortex, magnetic monopole, and Yang-Mills instanton (wall-vortex-monopole-instanton) using the effective theory technique or moduli approximation. Removing some solitons from such a composite, we obtain all possible composite solitons in the form of solitons within a soliton, including all the previously known configurations, yielding relations among topological solitons.
This talk is based on Phys.Rev.D 105 (2022) 10, 105006, e-Print: 2202.
03929 [hep-th].

The information loss paradox associated with black hole evaporation is an unresolved problem in modern theoretical physics. We consider the evolution of the black hole entanglement entropy via the Euclidean path integral of the quantum state under the semi-classical approximation. We argue that there exist Euclidean instantons that mediate the tunneling from a black hole geometry to a trivial geometry where all the black hole mass is carried away as radiation. By taking into account the multiple classical histories resulting from the tunneling, we recover the Page curve for the entanglement entropy, albeit being modified, with its maximum largely exceeding the Bekenstein-Hawking bound.

We discuss how to construct non-abelian chiral gauge theories with anomaly-free multiplets of Weyl fermions on the lattice without breaking the gauge invariance or violating any other fundamental principle. There are two approaches for this purpose:
1.To establish the integrability condition for the chiral determinant of overlap Weyl fermions
2.To gap out the mirror degrees of freedom of overlap Dirac fermions (Domain-wall fermions) with certain (boundary) interaction terms
In the former case, the integrability condition for the chiral determinant of overlap Weyl fermions can be formulated with five-, and six-dimensional lattice Domain-wall fermions. This formulation of the integrability condition is in parallel to the recent cobordism classification of global ‘t Hooft anomaly with the η-invariant based on the Dai-Freed theorem and the APS index theorem in the continuum theory. In the latter case, the required condition for the interaction terms is given by the complete cancellation of ‘t Hooft anomalies. We discuss the recent results on these two approaches.

Recently, Hoshina, Fujii, and Kikukawa [1] pointed out that the naive lattice gauge theory action in Minkowski signature does not result in a unitary theory in the continuum limit, and Kanwar and Wagman [2] proposed alternative lattice actions to the Wilson action without divergences. We here show that the subtlety can be understood from the asymptotic expansion of the modified Bessel function, which has been discussed for path integral of compact variables in nonrelativistic quantum mechanics [3,4]. The essential ingredient for defining the appropriate continuum theory is the iε prescription, which we show is applicable also for the Wilson action. It is here important that the iε should be implemented for both timelike and spacelike plaquettes. We then argue that such iε can be given a physical meaning that they remove singular paths having nontrivial winding for an infinitesimal time evolution that do not have corresponding paths in the continuum. Such point of view is only apparent in systems with compact variables as lattice gauge theories. This talk is based on [5].
[1] H. Hoshina, H. Fujii and Y. Kikukawa, “Schwinger-Keldysh formalism for Lattice Gauge Theories,” PoS LATTICE2019, 190 (2020)
[2] G. Kanwar and M. L. Wagman, “Real-time lattice gauge theory actions: Unitarity, convergence, and path integral contour deformations,” Phys. Rev. D 104, no.1, 014513 (2021) [arXiv:2103.02602 [hep-lat]]
[3] W. Langguth and A. Inomata, “Remarks on the Hamiltonian path integral in polar coordinates,” J. Math. Phys. 20, 499-504 (1979)
[4] M. Bohm and G. Junker, “Path integration over compact and noncompact rotation groups,” J. Math. Phys. 28, 1978-1994 (1987)
[5] N. M. “Comment on the subtlety of defining real-time path integral in lattice gauge theories,” [arXiv:2206.00865 [hep-lat]]

Dimensionally reduced effective theories (EFT) have been very successful for studying the thermodynamics of non-Ablian gauge theories.
The dimensionally reduced, long distance, effective theories for thermal QCD are electrostatic (“EQCD”) and magnetostatic QCD (“MQCD”). After discussing the latest limits of the EFT construction, I will focus on recent advancements to understand jet modification using non-perturbative input from EQCD.

Jet-medium interactions in the Quark-Gluon Plasma can receive large non-perturbative infrared contributions. These contributions affect transverse jet momentum broadening and jet quenching. Both are influenced by the modified in-medium dispersion of jets encoded in their asymptotic mass. An IR-safe computation of the latter requires subtracting the unphysical UV limit of EQCD, and supplying the correct UV limit obtained from Minkowski-time QCD. We perform the first step of this procedure in calculating the necessary operators in EQCD both analytically and on the lattice. We find compelling agreement of the two methods in the ultraviolet regime.

We demonstrate a tensor renormalization group (TRG) calculation for a two-dimensional Lorentzian model of quantum Regge calculus (QRC). This model is expressed in terms of a tensor network by discretizing the continuous edge lengths of simplicial manifolds and identifying them as tensor indices.
The expectation value of space-time area, which is obtained through the higher-order TRG method, nicely reproduces the exact value. The Lorentzian model does not have the spike configuration that was an obstacle in the Euclidean QRC, but it still has a length-divergent configuration called a pinched geometry. We find a possibility that the pinched geometry is suppressed by checking the average length squared in the limit where the number of simplices is large. This implies that the Lorentzian model may describe smooth geometries. Our results also indicate that TRG is a promising approach to numerical study of simplicial quantum gravity.

We discuss quantum improvements of black holes in asymptotic safety scenario. In this scenario, the Newton coupling depends on an energy scale, which must then be identified with a certain length scale. Due to this “scale identification,” in a small scale, e.g., near the singularity, a quantum mechanically corrected or “quantum improved” geometry behaves significantly differently from its classical counterpart. For example, the quantum improved Schwarzschild black hole is perfectly regular near the center. However, when considering more general black holes, whether a singularity is resolved or not depends on the choice of possible scale identification. Furthermore, if applying the same scale identification as in the Schwarzschild case for a rotating black hole, the quantum improved rotating black hole becomes inconsistent with the thermodynamic laws. In this talk, we first briefly review quantum improvement of black holes in asymptotic safety scenario and the problem in possible choice of scale identifications. We then propose that the consistency with the first law of black hole thermodynamics is the guiding principle for a physically sensible choice of scale identifications. This principle leads us to show that the running Newton coupling should be a function of the horizon area at least near the horizon, and also to find a universal formula for the quantum entropy.

Some say that the high density EOS is only poorly constrained, but this statement is just like a pump and dump. If you look at the QCD calculations you may find huge uncertainty, but this uncertainty extends to the direction to make the EOS softer below the conformal bound that is already very soft. This implies an intriguing physics picture that interacting nuclear matter quickly approaches the conformal EOS and it is saturated by weakly interacting quark matter after smooth crossover where the speed of sound can have a peak. Such considerations lead us to a well constrained and very likely EOS with quark matter crossover. Then, the question is whether such a smooth change without the frequently-postulated first-order discontinuity can be detectable by the gravitational wave observation or not, and our recent analysis gives a positive answer.

ヘテロティック弦は10次元時空ですでに非可換ゲージ対称性を持つ超弦理論であり、80年代、現在のような宇宙観測結果もない時代に精力的に研究されました。しかしD-ブレインの認識以降、それを含まないヘテロティック理論は弦理論研究の主流ではなくなっていましたが、主要なGUTゲージ群や素粒子１世代SO(10)のスピナー表現物質を自然に導出するという性質は、現代の弦理論による模型構築においても大きな利点です。
中島さんには、現代的な視点から、このようなヘテロティック理論について、基本的なことから解説していただきたいと思います。