17073222
Errata and Addenda to ``Anomaly Cancellation Condition in Lattice Gauge Theory''
We correct some intermediate expressions and arguments in hep-lat/0002009 (Nucl. Phys. B 585 (2000) 471--513). The main results do not change. We also mention some additional observations, including a constraint on a coefficient of the possible nontrivial anomaly which was not given in the paper.
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.
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.
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.
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.
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.
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.
15548726
Postbounce Evolution of Core-Collapse Supernovae: Long-Term Effects of the Equation of State
We study the evolution of a supernova core from the beginning of the gravitational collapse of a 15 M☉ star up to 1 s after core bounce. We present results of spherically symmetric simulations of core-collapse supernovae by solving general relativistic ν-radiation hydrodynamics in the implicit time differencing. We aim to explore the evolution of shock waves in the long term and investigate the formation of proto-neutron stars together with supernova neutrino signatures. These studies are done to examine the influence of the equation of state (EOS) on the postbounce evolution of shock waves in the late phase and the resulting thermal evolution of proto-neutron stars. We compare two sets of EOSs, namely, those by Lattimer and Swesty (LS-EOS) and by Shen et al. (SH-EOS). We found that, for both EOSs, the core does not explode and the shock wave stalls similarly in the first 100 ms after bounce. A revival of the shock wave does not occur even after a long period in either case. However, the recession of the shock wave appears different beyond 200 ms after bounce, having different thermal evolution of the central core. A more compact proto-neutron star is found for LS-EOS than SH-EOS with a difference in the central density by a factor of ~2 and a difference of ~10 MeV in the peak temperature. The resulting spectra of supernova neutrinos are different to an extent that may be detectable by terrestrial neutrino detectors.
122742819
Implications of the Discovery of Sub-Millisecond Pulsar in SN1987A
3Me companion object, it seems hard to account for such an object in the scenario of the supernova explosion. We estim;tte the magnetic field, ellipticity and the mass of the neutron star and also the period of glitches.
118745211
R-Process Nucleosynthesis In Neutrino-Driven Winds From A Typical Neutron Star With M = 1.4 Msun
We study the effects of the outer boundary conditions in neutrino-driven winds on the r-process nucleosynthesis. We perform numerical simulations of hydrodynamics of neutrino-driven winds and nuclear reaction network calculations of the r-process. As an outer boundary condition of hydrodynamic calculations, we set a pressure upon the outermost layer of the wind, which is approaching toward the shock wall. Varying the boundary pressure, we obtain various asymptotic thermal temperature of expanding material in the neutrino-driven winds for resulting nucleosynthesis. We find that the asymptotic temperature slightly lower than those used in the previous studies of the neutrino-driven winds can lead to a successful r-process abundance pattern, which is in a reasonable agreement with the solar system r-process abundance pattern even for the typical proto-neutron star mass Mns ~ 1.4 Msun. A slightly lower asymptotic temperature reduces the charged particle reaction rates and the resulting amount of seed elements and lead to a high neutron-to-seed ratio for successful r-process. This is a new idea which is different from the previous models of neutrino-driven winds from very massive (Mns ~ 2.0 Msun) and compact (Rns ~ 10 km) neutron star to get a short expansion time and a high entropy for a successful r-process abundance pattern. Although such a large mass is sometimes criticized from observational facts on a neutron star mass, we dissolve this criticism by reconsidering the boundary condition of the wind. We also explore the relation between the boundary condition and neutron star mass, which is related to the progenitor mass, for successful r-process.
14396526
Properties of a relativistic equation of state for collapse-driven supernovae
Abstract We study characteristics of the relativistic equation of state (EOS) for collapse-driven supernovae, which is derived by relativistic nuclear many body theory. Recently the relativistic EOS table has become available as a new complete set of physical EOS for numerical simulations of supernova explosion. We examine this EOS table by using general relativistic hydrodynamics of the gravitational collapse and bounce of supernova cores. In order to study dense matter in dynamical situation, we perform simplified calculations of core collapse and bounce by following adiabatic collapse with the fixed electron fraction for a series of progenitor models. This is intended to give us “approximate models” of prompt explosion. We investigate the profiles of thermodynamical quantities and the compositions during collapse and bounce. We also perform the calculations with the Lattimer–Swesty EOS to compare the properties of dense matter. As a measure of the stiffness of the EOS, we examine the explosion energy of the prompt explosion with electron capture totally suppressed. We study the derivative of the thermodynamical quantities obtained by the relativistic EOS to discuss the convective condition in neutron-rich environment, which may be important in the delayed explosion.