6061342
CP breaking in lattice chiral gauge theories
The CP symmetry is not manifestly implemented for the local and doubler-free Ginsparg-Wilson operator in lattice chiral gauge theory. We precisely identify where the effects of this CP breaking appear. We show that they appear in: (I) Overall constant phase of the fermion generating functional. (II) Overall constant coefficient of the fermion generating functional. (III) Fermion propagator appearing in external fermion lines and the propagator connected to Yukawa vertices. The first effect appears from the transformation of the path integral measure and it is absorbed into a suitable definition of the constant phase factor for each topological sector; in this sense there appears no ``CP anomaly''. The second constant arises from the explicit breaking in the action and it is absorbed by the suitable weights with which topological sectors are summed. The last one in the propagator is inherent to this formulation and cannot be avoided by a mere modification of the projection operator, for example, in the framework of the Ginsparg-Wilson operator. This breaking emerges as an (almost) contact term in the propagator when the Higgs field, which is treated perturbatively, has no vacuum expectation value. In the presence of the vacuum expectation value, however, a completely new situation arises and the breaking becomes intrinsically non-local, though this breaking may still be removed in a suitable continuum limit. This non-local CP breaking is expected to persist for a non-perturbative treatment of the Higgs coupling.
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.
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.
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.
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.
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.
18029655
Influence of the symmetry energy on the birth of neutron stars and supernova neutrinos
We study the influence of the symmetry energy of the equation of state on the thermal evolution of protoneutron stars and the properties of supernova neutrinos by the numerical simulations after the protoneutron stars are formed. As for the equation of state (EOS) of nuclear matter, we take two EOS's with different symmetry energies obtained by the relativistic mean field theory. We find the symmetry energy plays the essential role on the evolution of lepton profiles and the neutrino fluxes.
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.
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.
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.