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.
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.
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.
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.
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.
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.
123694356
DARK ENERGY MODELS AND SUPERNOVA RELIC NEUTRINOS
Recent cosmological observations show that the unknown energy element called dark energy dominates in the universe. In this letter, we investigate to what extent dark energy models influence supernova relic neutrino (SRN) spectra when the supernova rate could be determined by direct counting and discuss the possibility to distinguish dark energy models using future observation of SRN. We found that the total number of SRN events in GCG model will be larger than those in ΛCDM and holographic dark energy models by 20%. As a result, we find a possibility to distinguish GCG model from ΛCDM and holographic dark energy models using observation of SRN. SRN should be a unique probe into dark energy models and will play complementary roles to other observables.
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.
124262809
Statistical Analysis of the Neutrino Burst from SN1987A
Les 3 derniers evenements observes au detecteur de Kamiokande lors du sursaut de neutrino depuis la supernova SN 1987A sont arrives avec 7 secondes de retard apres les autres. La probabilite d'une telle observation est calculee dans le cadre du modele standard de refroidissement du cœur de la supernova. On obtient une valeur tout au plus egale a 2%
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.