17223313
CHIRAL ANOMALIES IN THE REDUCED (OR MATRIX) MODEL
We show that, with an appropriate choice of a Dirac operator, there is a remnant of chiral anomalies in the reduced model in which there is no coordinate dependences of the gauge field. This result is obtained by exploring a topological nature of chiral anomalies associated to Ginsparg-Wilson-type lattice Dirac operators.
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.
15095584
A local formulation of lattice Wess-Zumino model with exact U(1)R symmetry
A lattice Wess-Zumino model is formulated on the basis of Ginsparg-Wilson fermions. In perturbation theory, our formulation is equivalent to the formulation by Fujikawa and Ishibashi and by Fujikawa. Our formulation is, however, free from a singular nature of the latter formulation due to an additional auxiliary chiral supermultiplet on a lattice. The model posssesses an exact U(1)R symmetry as a supersymmetric counterpart of the L?scher lattice chiral U(1) symmetry. A restration of the supersymmetric Ward-Takahashi identity in the continuum limit is analyzed in renormalized perturbation theory. In the one-loop level, a supersymmetric continuum limit is ensured by suitably adjusting a coefficient of a single local term *. The non-renormalization theorem holds to this order of perturbation theory. In higher orders, on the other hand, coefficents of local terms with dimension ? 4 that are consistent with the U(1)R symmetry have to be adjusted for a supersymmetric continuum limit. The origin of this complexicity in higher-order loops is clarified on the basis of the Reisz power counting theorem. Therefore, from a view point of supersymmetry, the present formulation is not quite better than a lattice Wess-Zumino model formulated by using Wilson fermions, although a number of coefficients which require adjustment is much less due to the exact U(1)R symmetry. We also comment on an exact non-linear fermionic symmetry which corresponds to the one studied by Bonini and Feo; an existence of this exact symmetry itself does not imply a restoration of supersymmetry in the continuum limit without any adjustment of parameters.
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.
121429699
BRS current and related anomalies in two-dimensional gravity and string theories
The BRS currents in two-dimensional gravity and supergravity theories, which are related to string theory, contain anomalous terms. The origin of these anomalies can be neatly understood in a carefully defined path integral. We present the detailed calculations of these BRS and related anomalies in the holomorphic or anti-holomorphic sector separately in the conformal gauge. One-loop renormalization of the Liouville action becomes transparent in our formalation. We identify a BRS invariant BRS current (and thus nil-potent charge) and a conformally invariant ghost number current by incorporating the dynamical Weyl freedom explicitly. The formal path integral construction of various composite operators is also checked by using the operator product technique. Implications of these BRS analyses on possible non-critical string theories at d < 26 or d < 10 are briefly discussed.
118715119
EFFECTS OF RESISTIVITY ON MAGNETIZED CORE-COLLAPSE SUPERNOVAE
We studied the role of turbulent resistivity in the core-collapse of a strongly magnetized massive star, carrying out two-dimensional resistive-MHD simulations. Three cases with different initial strengths of magnetic field and rotation are investigated: (1) a strongly magnetized rotating core, (2) a moderately magnetized rotating core, and (3) a very strongly magnetized non-rotating core. In each case, one ideal-MHD model and two resistive-MHD models are computed. As a result of these computations, each model shows an eruption of matter assisted by magnetic acceleration (and also by centrifugal acceleration in the rotating cases). We found that resistivity attenuates the explosion in cases 1 and 2, while it enhances the explosion in case 3. We also found that in the rotating cases, the main mechanisms for the amplification of a magnetic field in the post-bounce phase are an outward advection of the magnetic field and a twisting of poloidal magnetic field lines by differential rotation, which are somewhat dampened down with the presence of resistivity. Although magnetorotational instability seems to occur in the rotating models, it plays only a minor role in magnetic field amplification. Another impact of resistivity is that on the aspect ratio. In the rotating cases, a large aspect ratio of the ejected matter, >2.5, attained in an ideal-MHD model is reduced to some extent in a resistive model. These results indicate that resistivity possibly plays an important role in the dynamics of strongly magnetized supernovae.
118538455
Neutrino oscillation and expected event rate of supernova neutrinos in the adiabatic explosion model
We study how the influence of the shock wave appears in neutrino oscillations and the neutrino spectrum by using the density profile of the adiabatic explosion model of a core-collapse supernova, which is calculated in an implicit Lagrangian code for general relativistic spherical hydrodynamics. We calculate expected event rates of neutrino detection at Super-Kamiokande (SK) and Sudbury Neutrino Observatory (SNO) for various ${\ensuremath{\theta}}_{13}$ values and both normal and inverted hierarchies. The predicted event rates of ${\overline{\ensuremath{\nu}}}_{e}$ and ${\ensuremath{\nu}}_{e}$ depend on the mixing angle ${\ensuremath{\theta}}_{13}$ for the inverted and normal mass hierarchies, respectively, and the influence of the shock wave appears for about 2\char21{}8 s when ${sin﻿}^{2}2{\ensuremath{\theta}}_{13}$ is larger than ${10}^{\ensuremath{-}3}$. These neutrino signals for the shock-wave propagation is decreased by $\ensuremath{\lesssim}30%$ for ${\overline{\ensuremath{\nu}}}_{e}$ in inverted hierarchy (SK) or by $\ensuremath{\lesssim}15%$ for ${\ensuremath{\nu}}_{e}$ in normal hierarchy (SNO) compared with the case without shock. The obtained ratio of the total event for high-energy neutrinos ($20\text{ }\text{ }\mathrm{MeV}\ensuremath{\leqq}{E}_{\ensuremath{\nu}}\ensuremath{\leqq}60\text{ }\text{ }\mathrm{MeV}$) to low-energy neutrinos ($5\text{ }\text{ }\mathrm{MeV}\ensuremath{\lesssim}{E}_{\ensuremath{\nu}}\ensuremath{\leqq}20\text{ }\text{ }\mathrm{MeV}$) is consistent with the previous studies in schematic semianalytic or other hydrodynamic models of the shock propagation. The time dependence of the calculated ratio of the event rates of high-energy neutrinos to the event rates of low-energy neutrinos is a very useful observable which is sensitive to ${\ensuremath{\theta}}_{13}$ and mass hierarchies. Namely, the time-dependent ratio shows a clearer signal of the shock-wave propagation that exhibits a remarkable decrease by at most a factor of $\ensuremath{\sim}2$ for ${\overline{\ensuremath{\nu}}}_{e}$ in inverted hierarchy (SK), whereas it exhibits a smaller change by $\ensuremath{\sim}10%$ for ${\ensuremath{\nu}}_{e}$ in normal hierarchy (SNO). Observing the time-dependent high-energy to low-energy ratio of the neutrino events thus would provide a piece of very useful information to constrain ${\ensuremath{\theta}}_{13}$ and mass hierarchy and eventually help understand how the shock wave propagates inside the star.
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.
122310560
NEUTRINOS PROM PROTONEUTRON STARS WITH VARIOUS EQUATION OF STATES
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.