119194920
Bosonization in the path integral formulation
We establish the direct $d=2$ on-shell bosonization $\psi_{L}(x_{+})=e^{i\xi(x_{+})}$ and $\psi_{R}^{\dagger}(x_{-})=e^{i\xi(x_{-})}$ in path integral formulation by deriving the off-shell relations $\psi_{L}(x)\psi_{R}^{\dagger}(x)=\exp[i\xi(x)]$ and $\psi_{R}(x)\psi_{L}^{\dagger}(x)=\exp[-i\xi(x)]$. Similarly, the on-shell bosonization of the bosonic commuting spinor, $\phi_{L}(x_{+})=ie^{-i\xi(x_{+})}\partial^{+}e^{-i\chi(x_{+})}$, $\phi^{\dagger}_{R}(x_{-})=e^{-i\xi(x_{-})-i\chi(x_{-})}$ and $\phi_{R}(x_{-})=ie^{i\xi(x_{-})}\partial^{-}e^{+i\chi(x_{-})}$, $\phi^{\dagger}_{L}(x_{+})=e^{i\xi(x_{+})+i\chi(x_{+})}$, is established in path integral formulation by deriving the off-shell relations $\phi_{L}(x)\phi^{\dagger}_{R}(x)=ie^{-i\xi(x)}\partial^{+}e^{-i\chi(x)}$ and $\phi_{R}(x)\phi^{\dagger}_{L}(x)=ie^{i\xi(x)}\partial^{-}e^{i\chi(x)}$.
118409043
Euclidean lattice simulation for dynamical supersymmetry breaking
The global supersymmetry is spontaneously broken if and only if the ground-state energy is strictly positive. We propose to use this fact to observe the spontaneous supersymmetry breaking in Euclidean lattice simulations. For lattice formulations that possess a manifest fermionic symmetry, there exists a natural choice of a Hamiltonian operator that is consistent with a topological property of the Witten index. We confirm validity of our idea in models of the supersymmetric quantum mechanics. We then examine a possibility of a dynamical supersymmetry breaking in the two-dimensional $\mathcal{N}=(2,2)$ super Yang-Mills theory with the gauge group $\mathrm{SU}(2)$, for which the Witten index is unknown. Differently from a recent conjectural claim, our numerical result tempts us to conclude that supersymmetry is not spontaneously broken in this system.
119483534
Axial anomaly in the reduced model: Higher representations☆
Abstract The topological charge in the U( N ) vector-like reduced model can be defined by using the overlap Dirac operator. We obtain its large N limit for a fermion in a general gauge-group representation under a certain restriction of gauge field configurations which is termed U(1) embedding.
14282824
SUSY WT identity in a lattice formulation of 2D N = (2, 2) SYM
Abstract We address some issues relating to a supersymmetric (SUSY) Ward–Takahashi (WT) identity in Sugino's lattice formulation of two-dimensional (2D) N = ( 2 , 2 ) SU ( k ) supersymmetric Yang–Mills theory (SYM). A perturbative argument shows that the SUSY WT identity in the continuum theory is reproduced in the continuum limit without any operator renormalization/mixing and tuning of lattice parameters. As application of the lattice SUSY WT identity, we show that a prescription for the Hamiltonian density in this lattice formulation, proposed by Kanamori, Sugino and Suzuki, is justified also from a perspective of an operator algebra among correctly-normalized supercurrents. We explicitly confirm the SUSY WT identity in the continuum limit to the first nontrivial order in a semi-perturbative expansion.
119414305
Anomalies, local counter terms and bosonization
We re-examine the issue of local counter terms in the analysis of quantum anomalies. We analyze two-dimensional theories and show that the notion of local counter terms need to be carefully defined depending on the physics contents such as whether one is analyzing gauge theory or bosonization. It is shown that a part of the Jacobian, which is apparently spurious and eliminated by a local counter term corresponding to the mass term of the gauge field in gauge theory, cannot be removed by a local counter term and plays a central role by giving the kinetic term of the bosonized field in the context of path integral bosonization.
119213970
Renormalizability of the gradient flow in the 2D O(N) non-linear sigma model
It is known that the gauge field and its composite operators evolved by the Yang--Mills gradient flow are ultraviolet (UV) finite without any multiplicative wave function renormalization. In this paper, we prove that the gradient flow in the 2D $O(N)$ non-linear sigma model possesses a similar property: The flowed $N$-vector field and its composite operators are UV finite without multiplicative wave function renormalization. Our proof in all orders of perturbation theory uses a $(2+1)$-dimensional field theoretical representation of the gradient flow, which possesses local gauge invariance without gauge field. As application of the UV finiteness of the gradient flow, we construct the energy--momentum tensor in the lattice formulation of the $O(N)$ non-linear sigma model that automatically restores the correct normalization and the conservation law in the continuum limit.
119251795
Global Simulations of Magnetorotational Instability in the Collapsed Core of a Massive Star
We performed the first global numerical simulations of magnetorotational instability from a sub-magnetar-class seed magnetic field in core-collapse supernovae. As a result of axisymmetric ideal MHD simulations, we found that the magnetic field is greatly amplified to magnetar-class strength. In the saturation phase, a substantial part of the core is dominated by turbulence, and the magnetic field possesses dominant large-scale components, comparable to the size of a proto-neutron star. A pattern of coherent channel flows, which generally appears during the exponential growth phase in previous local simulations, is not observed in our global simulations. While the approximate convergence in the exponential growth rate is attained by increasing spatial resolution, that of the saturation magnetic field is not achieved due to still large numerical diffusion. Although the effect of the magnetic field on the dynamics is found to be mild, a simulation with a high enough resolution might result in a larger impact.
123694356
DARK ENERGY MODELS AND SUPERNOVA RELIC NEUTRINOS
Recent cosmological observations show that the unknown energy element called dark energy dominates in the universe. In this letter, we investigate to what extent dark energy models influence supernova relic neutrino (SRN) spectra when the supernova rate could be determined by direct counting and discuss the possibility to distinguish dark energy models using future observation of SRN. We found that the total number of SRN events in GCG model will be larger than those in ΛCDM and holographic dark energy models by 20%. As a result, we find a possibility to distinguish GCG model from ΛCDM and holographic dark energy models using observation of SRN. SRN should be a unique probe into dark energy models and will play complementary roles to other observables.
118431737
A new baryonic equation of state at sub-nuclear densities for core-collapse simulations
We calculate a new equation of state for baryons at sub-nuclear densities meant for the use in core-collapse simulations of massive stars. The abundances of various nuclei are obtained together with the thermodynamic quantities. The formulation is the nuclear statistical equilibrium description and the liquid drop approximation of nuclei. The model free energy to minimize is calculated by relativistic mean field theory for nucleons and the mass formula for nuclei with atomic number up to ~1000. We have also taken into account the pasta phase, thanks to which the transition to uniform nuclear matter in our equation of state (EOS) occurs in the conventional manner: nuclei are not dissociated into nucleons but survive right up to the transition to uniform nuclear matter. We find that the free energy and other thermodynamical quantities are not very different from those given in the H. Shen's EOS, one of the standard EOSs that adopt the single nucleus approximation. On the other hand, the average mass is systematically different, which may have an important ramification to the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores. It is also interesting that the root mean square of the mass number is not very different from the average mass number, since the former is important for the evaluation of coherent scattering rates on nuclei but has been unavailable so far. The EOS table is currently under construction, which will include the weak interaction rates.
118715119
EFFECTS OF RESISTIVITY ON MAGNETIZED CORE-COLLAPSE SUPERNOVAE
We studied the role of turbulent resistivity in the core-collapse of a strongly magnetized massive star, carrying out two-dimensional resistive-MHD simulations. Three cases with different initial strengths of magnetic field and rotation are investigated: (1) a strongly magnetized rotating core, (2) a moderately magnetized rotating core, and (3) a very strongly magnetized non-rotating core. In each case, one ideal-MHD model and two resistive-MHD models are computed. As a result of these computations, each model shows an eruption of matter assisted by magnetic acceleration (and also by centrifugal acceleration in the rotating cases). We found that resistivity attenuates the explosion in cases 1 and 2, while it enhances the explosion in case 3. We also found that in the rotating cases, the main mechanisms for the amplification of a magnetic field in the post-bounce phase are an outward advection of the magnetic field and a twisting of poloidal magnetic field lines by differential rotation, which are somewhat dampened down with the presence of resistivity. Although magnetorotational instability seems to occur in the rotating models, it plays only a minor role in magnetic field amplification. Another impact of resistivity is that on the aspect ratio. In the rotating cases, a large aspect ratio of the ejected matter, >2.5, attained in an ideal-MHD model is reduced to some extent in a resistive model. These results indicate that resistivity possibly plays an important role in the dynamics of strongly magnetized supernovae.
118114185
Neutrino signal of supernova shock wave propagation:MSW distortion of the spectra and neucleosynthesis
S. Kawagoe ∗ab, H. Suzuki c, K. Sumiyoshi bd, H. Yamadae and T. Kajino ab f aDepartment of Astronomical Science, School of Physical Sciences, The Graduate University for Advanced Studies(SOKENDAI) 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan bNational Astronomical Observatory of Japan 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan cDepartment of Physics, Faculty of Science and Technology, Tokyo University of Science 2641 Yamazaki, Noda, Chiba 278-8510, Japan dNumazu College of Technology 3600 Ooka, Numazu, Shizuoka 410-8501, Japan eDepartment of Physics, Faculty of Science and Engineering, Waseda University 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan f Department of Astronomy, Graduate School of Science, University of Tokyo 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan E-mail: shiou@th.nao.ac.jp