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.
14173807
Ginsparg–Wilson operators and a no-go theorem
Abstract If one uses a general class of Ginsparg–Wilson operators, it is known that CP symmetry is spoiled in chiral gauge theory for a finite lattice spacing and the Majorana fermion is not defined in the presence of chiral symmetric Yukawa couplings. We summarize these properties in the form of a theorem for the general Ginsparg–Wilson relation.
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.
16738479
Gauge Anomaly Associated with the Majorana Fermion in 8k + 1 Dimensions
Using an elementary method, we show that an odd number of Majorana fermions in 8k + 1 dimensions suffer from a gauge anomaly that is analogous to the Witten global gauge anomaly. This anomaly cannot be removed without sacrificing the perturbative gauge invariance. Our construction of higher-dimensional examples (k > 1) makes use of the SO(8) instanton on S 8 .
119574601
Shock wave propagation in prompt supernova explosion and the MSW effect of neutrino
The MSW effect of supernova neutrino is one of foci of recent neutrino astrophysics. It is still an open question how the shock wave propagation affects the neutrino oscillation. Using an implicit Lagrangian code for general relativistic spherical hydrodynamics, we succeeded in numerical simulations of breakout of shock wave propagation through the stellar envelope. We first discuss our successful result of shock wave propagation which is generated by adiabatic collapse of iron core, and compare with non-adiabatic models. Secondly, we apply our model to the neutrino oscillation and calculate survival probabilities of three light-neutrino families. We discuss how the flux and energy spectrum of each neutrino species can change due to the MSW effect.
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.
118647169
New equations of state based on the liquid drop model of heavy nuclei and quantum approach to light nuclei for core-collapse supernova simulations
We construct new equations of state for baryons at subnuclear densities for the use in core-collapse simulations of massive stars. The abundance of various nuclei is obtained together with thermodynamic quantities. A model free energy is constructed, based on the relativistic mean field theory for nucleons and the mass formula for nuclei with the proton number up to ~1000. The formulation is an extension of the previous model, in which we adopted the liquid drop model to all nuclei under the nuclear statistical equilibrium. We reformulate the new liquid drop model so that the temperature dependences of bulk energies could be taken into account. Furthermore, we extend the region in the nuclear chart, in which shell effects are included, by using theoretical mass data in addition to experimental ones. We also adopt a quantum-theoretical mass evaluation of light nuclei, which incorporates the Pauli- and self-energy shifts that are not included in the ordinary liquid drop model. The pasta phases for heavy nuclei are taken into account in the same way as in the previous model. We find that the abundances of heavy nuclei are modified by the shell effects of nuclei and temperature dependence of bulk energies. These changes may have an important effect on the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores. The abundances of light nuclei are also modified by the new mass evaluation, which may affect the heating and cooling rates of supernova cores and shocked envelopes.
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.
17130454
Dynamics and Neutrino Signal of Black Hole Formation in Nonrotating Failed Supernovae. II. Progenitor Dependence
We study the progenitor dependence of black hole formation and its associated neutrino signal due to the gravitational collapse of a nonrotating massive star, following on our previous study of a single progenitor model. We aim to clarify whether the dynamical evolution toward black hole formation occurs in the same manner for different progenitors and to examine whether the characteristic of neutrino bursts having short duration and rapidly increasing average energies is a general one. We perform numerical simulations using general relativistic neutrino radiation hydrodynamics to follow the dynamical evolution from the collapse of 40 and 50 M☉ presupernova models to black hole formation via contracting proto-neutron stars. For the three progenitor models studied in this paper, we find that black hole formation occurs ~0.4-1.5 s after core bounce through an increase of the proto-neutron star mass, accompanied by a short and energetic neutrino burst. The density profile of the progenitor is important in determining the accretion rate onto the proto-neutron star and, therefore, the duration of the neutrino burst. We compare the neutrino bursts of black hole-forming events from different progenitors and discuss whether they can be used to probe clearly the progenitor and the dense matter.