14739225
Some physics of the two-dimensional N = (2, 2) supersymmetric Yang-Mills theory: Lattice Monte Carlo study
Abstract We illustrate some physical application of a lattice formulation of the two-dimensional N = ( 2 , 2 ) supersymmetric SU ( 2 ) Yang–Mills theory with a (small) supersymmetry breaking scalar mass. Two aspects, power-like behavior of certain correlation functions (which implies the absence of the mass gap) and the static potential V ( R ) between probe charges in the fundamental representation, are considered. For the latter, for R ≲ 1 / g , we observe a linear confining potential with a finite string tension. This confining behavior appears distinct from a theoretical conjecture that a probe charge in the fundamental representation is screened in two-dimensional gauge theory with an adjoint massless fermion, although the static potential for R ≳ 1 / g has to be systematically explored to conclude real asymptotic behavior in large distance.
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.
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.
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.
118908804
Multigroup simulation of protoneutron star cooling and neutrino spectra
14724846
An approach toward the successful supernova explosion by physics of unstable nuclei
We study the explosion mechanism of collapse-driven supernovae by numerical simulations with a new nuclear EOS based on unstable nuclei. We report new results of simulations of general relativistic hydrodynamics together with the Boltzmann neutrino-transport in spherical symmetry. We adopt the new data set of relativistic EOS and the conventional set of EOS (Lattimer-Swesty EOS) to examine the influence on dynamics of core-collapse, bounce and shock propagation. We follow the behavior of stalled shock more than 500 ms after the bounce and compare the evolutions of supernova core.
125991530
Neutrino Transport in Type II Supernovae: Boltzmann Solver vs Monte Carlo Method
In this paper we discuss the results of extensive comparison of the Boltzmann solver recently developed by us and the Monte Carlo method coded by Janka. The aim of our project is to improve the treatment of the neutrino transfer and to study the neutrino reactions systematically, since the numerical treatment of neutrino transfer and neutrino reaction rates in the hot dense medium are two of the greatest uncertainties in the supernova simulations.
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.
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.