852398
A No-Go Theorem for the Majorana Fermion on a Lattice
be applied in 8k and 8k + 1 dimensions and, as a consequence, it is impossible to obtain a physically acceptable lattice formulation of the Majorana fermion in these dimensions. The authors then argued that this difficulty associated with the Majorana fermion is a manifestation of the global gauge anomaly 4) in 8k dimensions. 5) If this argument is correct, it will be extremely difficult to realize a physically acceptable lattice formulation of the Majorana fermion in these dimensions, because the difficulty has an intrinsic physical meaning. In the present paper, we formulate a variant of the Nielsen–Ninomiya no-go theorem 6),7) which states, under several assumptions, the impossibility of a lattice Majorana fermion in 8k and 8k + 1 dimensions. Our result, which is independent of the particular choice of the lattice Dirac operator and reflects the characteristics of the Clifford algebra in these dimensions, provides further evidence that the difficulty associated to the Majorana fermion in these dimensions has a deeper origin. In addition, we believe that this theorem will be useful in formulating a method to avoid the difficulty, because our theorem precisely specifies the assumptions that lead to the difficulty. One of these assumptions must be removed in order to realize a lattice formulation of the Majorana fermion, just as one usually circumvents the Nielsen–Ninomiya theorem by removing the assumption on chiral symmetry.
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.
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.
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.
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.
16888286
The fate of a neutron star just below the minimum mass: does it explode?
First results of numerical simulations are presented which compute the dynamical evolution of a neutron star with a mass slightly below the minimum stable mass by means of a new implicit (general relativistic) hydrodynamic code. We show that such a star first undergoes a phase of quasi-static expansion, caused by slow nuclear -decays, lasting for about 20 seconds, but then explodes violently. The kinetic energy of the explosion is around10 49 erg, the peak luminosity in electron anti-neutrinos is of order 10 52 erg/s, and the thermodynamic conditions of the expanding matter are favorable for r-process nucleosynthesis. These results are obtained for the Harrison-Wheeler equation of state and a simple and, possibly, unrealistic treatment of - decay rates and nuclear fission, which were adopted for compar- ison with previous works. However, we do not expect that the outcome will change qualitatively if more recent nuclear input physics is used. Although our study does not rely on a specific scenario of how a neutron star starting from a bigger (and stable) mass can reach the dynamical phase, we implicitly assume that the final mass-loss event happens on a very short time scale, i.e., on a time scale shorter than a sound-crossing time, by removing a certain amount of mass as an initial perturbation. This assumption im- plies that the star has no time to adjust its nuclear composition to the new mass through a sequence of quasi-equilibria. In the lat- ter case, however, there exists no stable configuration below the minimum mass, because the equation of state of fully catalyzed matter is too soft. Therefore, the dynamics of the explosion will not be too different from what we have obtained if different initial perturbations are assumed.
122249200
Constraining neutrino oscillation parameters with future observations of supernova neutrinos by various types of detectors
We evaluate the potential for constraining neutrino oscillation parameters with future observations of supernova neutrinos. For some selected oscillation parameters, we calculate the expected energy spectra and angular distributions of neutrino events in various detectors (Super-Kamiokande, ICARUS, KamLAND and IceCube) for an assumed galactic core-collapse supernova. We investigate to what extent the oscillation parameters could be constrained using χ2 analysis when the expected events are really observed.
118114185
Neutrino signal of supernova shock wave propagation:MSW distortion of the spectra and neucleosynthesis
S. Kawagoe ∗ab, H. Suzuki c, K. Sumiyoshi bd, H. Yamadae and T. Kajino ab f aDepartment of Astronomical Science, School of Physical Sciences, The Graduate University for Advanced Studies(SOKENDAI) 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan bNational Astronomical Observatory of Japan 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan cDepartment of Physics, Faculty of Science and Technology, Tokyo University of Science 2641 Yamazaki, Noda, Chiba 278-8510, Japan dNumazu College of Technology 3600 Ooka, Numazu, Shizuoka 410-8501, Japan eDepartment of Physics, Faculty of Science and Engineering, Waseda University 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan f Department of Astronomy, Graduate School of Science, University of Tokyo 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan E-mail: shiou@th.nao.ac.jp
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.