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.
115605822
Supernova neutrinos - multigroup simulations of neutrinos from protoneutron star.
492141
Manifestly Gauge Covariant Treatment of Lattice Chiral Fermion
We propose a lattice formulation of the chiral fermion which maximally respects the gauge symmetry and simultaneously is free of the unwanted species doublers. This is achieved by directly dealing with the lattice fermion propagator and the composite operators, rather than the lattice action and the fermionic determinant. The latter is defined as a functional integral of the expectation value of the gauge current operator with respect to the background gauge field. The gauge anomaly is characterized as a non-integrability of this integration process and, the determinant is defined only for anomaly free cases. Gauge singlet operators on the other hand are always regularized gauge invariantly. Some perturbative check is performed to confirm the gauge covariance and the absence of the doublers. This formulation can be applied rather straightforwardly to numerical simulations in the quenched approximation. ⋆ e-mail: hsuzuki@mito.ipc.ibaraki.ac.jp The chiral fermion on the lattice has refused the manifestly gauge invariant formulation [1]. There even exists the no-go theorem [2] for such an endeavor. In the continuum counterpart, the chiral fermion exhibits a curious phenomenon called the quantum anomaly [3], or more definitely the gauge anomaly [4]. The difficulty in the lattice chiral gauge theory seems to be a rather natural consequence of the gauge anomaly. Suppose that we start from a well regularized partition function or a fermionic determinant defined by a manifestly gauge invariant lattice fermion action. In the continuum limit, the gauge anomaly is realized as a gauge variation of the partition function. Therefore if the fermion content is not free of the gauge anomaly, the partition function is not gauge invariant. But this contradicts with the very gauge invariance of the formulation. There are mainly two possible ways out: One is the appearance of the species doublers which cancels the gauge anomaly [5]. Another is some pathology in the continuum limit such as the non-Lorentz covariance [6]. The trouble of the lattice regularization is that it always regularizes the ultraviolet divergence, even when a gauge invariant regularization is impossible due to the gauge anomaly. From the above reasoning, the appearance of the unwanted doublers are quite natural. But the problem in the conventional approach is of course that the doublers appear even in the anomaly free cases. Presumably, the ideal lattice formulation of the chiral fermion will be the one which distinguishes the anomaly free gauge representations from the anomalous ones. † That unknown lattice action should have a structure that can be written down, for example, for the spinor rep. of SO(4) but not for the fundamental rep. of SU(3), because the latter is anomalous. Such an ideal formulation seems to require a deeper understanding on the origin of the quantum anomaly, which is not available at present. In this article, we simply abandon a direct gauge invariant definition of the † Besides the perturbative anomaly, it should also explain the topological global anomaly [7] because the partition function is ill-defined with this anomaly.
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.
17171161
Observing dynamical supersymmetry breaking with euclidean lattice simulations
A strict positivity of the ground-state energy is a necessary and sufficient condition for spontaneous supersymmetry breaking. This ground-state energy may be directly determined from the expectation value of the Hamiltonian in the functional integral, defined with an antiperiodic temporal boundary condition for all fermionic variables. We propose to use this fact to observe the dynamical spontaneous supersymmetry breaking in Euclidean lattice simulations. If a lattice formulation possesses a manifestly preserved fermionic symmetry, there exists a natural choice of a Hamiltonian operator that is consistent with a topological nature of the Witten index. We numerically confirm the validity of our idea in models of supersymmetric quantum mechanics. We further examine the possibility of dynamical supersymmetry breaking in the two-dimensional N =( 2, 2) super Yang-Mills theory with the gauge group SU(2), for which the Witten index is unknown. Although statistical errors are still large, we do not observe positive ground-state energy, at least within one standard deviation. This prompts us to draw a different conclusion from a recent conjectural claim that supersymmetry is dynamically broken in this system.
16618542
Renormalon's contribution to effective couplings
When an asymptotically non-free theory possesses a mass parameter independent of the Λ parameter, the uv renormalon gives rise to nonperturbative contributions, to dimension-four operators and dimensionless couplings, thus has a "dual" effect of the instanton. We illustrate this phenomenon in O(N) symmetric massive λϕ4 model in the 1/N expansion. This effect of uv renormalon is briefly compared with nonperturbative corrections in the magnetic picture of the Seiberg–Witten theory.
14702420
Improved Convergence Proof of the Delta Expansion and Order Dependent Mappings
Abstract We improve and generalize in several accounts the recent rigorous proof of convergence of delta expansion–order dependent mappings (variational perturbation expansion) for the energy eigenvalues of quartic anharmonic oscillator. For the single-well oscillator the uniformity of convergence in g ∈[0, ∞] is proven. The convergence proof is extended also to complex values of g lying on a wide domain of the Riemann surface of E ( g ). Via the scaling relation a la Symanzik, this proves the convergence of delta expansion for the double well in the strong coupling regime (where the standard perturbation series is non Borel summable), as well as for the complex “energy eigenvalues” in certain metastable systems. Difficulties in extending the convergence proof to the cases of higher anharmonic oscillators are pointed out. Sufficient conditions for the convergence of delta expansion are summarized in the form of three general theorems, which should apply to a wide class of quantum mechanical and higher dimensional field theoretic systems.