17376955
Majorana and Majorana-Weyl fermions in lattice gauge theory
In various dimensional euclidean lattice gauge theories, we examine a compatibility of the Majorana decomposition and the charge conjugation property of lattice Dirac operators. In 8n and 1+8n dimensions, we find a difficulty to decompose a classical lattice action of the Dirac fermion into a system of the Majorana fermion and thus to obtain a factrized form of the Dirac determinant. Similarly, in 2+8n dimensions, there is a difficulty to decompose a classical lattice action of the Weyl fermion into a system of the Majorana-Weyl fermion and thus to obtain a factrized form of the Weyl determinant. Prescriptions based on the overlap formalism do not remove these difficulties. We argue that these difficulties are reflections of the global gauge anomaly associated to the real Weyl fermion in 8n dimensions. For this reason (besides other well-known reasons), a lattice formulation of the N = 1 super Yang-Mills theory in these dimensions is expected to be extremely difficult to find.
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.
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.
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.
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.
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.
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.
121630149
Constraints on oscillation parameters through the MSW effect of supernova neutrinos
We try to constrain the neutrino oscillation parameters by studying the MSW matter effect on supernova neutrinos. Using an implicit Lagrangian code for general relativistic spherical hydrodynamics (Yamada, 1997), we calculate the propagation of shock waves passing through the stellar envelopes over dozens of seconds, which is based on modeling the adiabatic collapse of iron core. We study how quantitatively the influence of the shock propagation appears in the deformation of neutrino energy spectrum. In addition, we are able to examine the θ13 dependence of time evolution of the neutrino detection rates at SK. Using our supernova model, we found that the MSW effect appears, at first, from low-energy region and moves toward high-energy region as the shock wave propagates. We find that the shock propagation has strong influence on the supernova neutrino oscillation through the evolution of density profile induced by the shock propagation.
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.