16822839
CALCULATION RULE FOR AOYAMA-TAMRA’S PRESCRIPTION FOR PATH INTEGRAL WITH QUANTUM TUNNELING
We derive a simple calculation rule for Aoyama-Tamra’s prescription for path integral with degenerated potential minima. Nonperturbative corrections due to the restricted functional space (fundamental region) can systematically be computed with this rule. It becomes manifest that the prescription might give Borel summable series for finite temperature (or volume) system with quantum tunneling, while the advantage is lost at zero temperature (or infinite volume) limit.
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.
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.
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.
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.
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.
18429697
Hydrodynamical study of neutrino-driven wind as an r-process site
We discuss the neutrino-driven wind from a proto-neutron star based on general-relat ivistic hydrodynamical simulations. We examine the properties of the neutrino-driven wind to explore the possibility of r-process nucleosynthesis. Numerical simulations involving neutrino heating and cooling processes were performed with the assumption of a constant neutrino luminosity by using realistic profiles of the protoneutron star (PNS) as well as simplified models. The dependence on the mass of PNS and the neutrino luminosity is presented systematically. Comparisons with analytic treatments in the previous studies are also given. In the cases with the realistic PNS, we have found that the entropy per baryon and the expansion time scale are neither high nor short enough for the r-process within the current assumptions. On the other hand, we have also found that the expansion time scale obtained by hydrodynamica l simulations is systematically shorter than that in the analytic solutions due to our proper treatment of the equation of state. This fact might lead to an increase in the neutron-to-seed ratio, which is suitable for the r-process in a neutrino-drive n wind. Indeed, in the case of massive and compact proto-neutron stars with high neutrino luminosities, the expansion time scale is found to be sufficiently short in hydrodynamica l simulations, and the r-process elements up to A ~ 200 are produced in the r-process network calculation.
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.
118984721
Gravitational radiation from rotational core collapse: Effects of magnetic fields and realistic equations of state
We perform a series of two-dimensional, axisymmetric, magnetohydrodynamic simulations of the rotational collapse of a supernova core. In order to calculate the waveforms of the gravitational wave, we derive the quadrupole formula including the contributions from the electromagnetic fields. Recent stellar evolution calculations imply that the magnetic fields of the toroidal components are much stronger than those of the poloidal ones at the presupernova stage. Thus, we systematically investigate the effects of the toroidal magnetic fields on the amplitudes and waveforms. Furthermore, we employ the two kinds of the realistic equation of states, which are often used in the supernova simulations. Then, we investigate the effects of the equation of states on the gravitational wave signals. With these computations, we find that the peak amplitudes are lowered by an order of 10% for the models with the strongest toroidal magnetic fields. However, the peak amplitudes are mostly within sensitivity range of laser interferometers such as TAMA and the first LIGO for a source at a distance of 10 kpc. Furthermore, we point out that the amplitudes of second peaks are still within the detection limit of the first LIGO for the source, although the characteristics of second peaks are reduced by the magnetic fields. We stress the importance of the detection, since it will give us information about the angular momentum distribution of massive evolved stars. When we compare the gravitational waves from the two realistic equation of states, significant differences are not found, except that the typical frequencies of the gravitational wave become slightly higher for the softer equation of state.
115605822
Supernova neutrinos - multigroup simulations of neutrinos from protoneutron star.
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.