Reply to Comment on Dirac spectral sum rules for QCD in three dimensions

I reply to the comment by Dr S. Nishigaki (hep-th/0007042) to my papers Phys. Rev. D61 (2000) 056005 and Phys. Rev. D62 (2000) 016005.Comment: 2 pages, LaTeX, no figure

Invariant Killing spinors in 11D and type II supergravities

We present all isotropy groups and associated $\Sigma$ groups, up to discrete identifications of the component connected to the identity, of spinors of eleven-dimensional and type II supergravities. The $\Sigma$ groups are products of a Spin group and an R-symmetry group of a suitable lower dimensional supergravity theory. Using the case of SU(4)-invariant spinors as a paradigm, we demonstrate that the $\Sigma$ groups, and so the R-symmetry groups of lower-dimensional supergravity theories arising from compactifications, have disconnected components. These lead to discrete symmetry groups reminiscent of R-parity. We examine the role of disconnected components of the $\Sigma$ groups in the choice of Killing spinor representatives and in the context of compactifications.Comment: 22 pages, typos correcte

Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories

Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, Abelian U(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev's toric code is a Z(2) lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge theory of the strong interactions between quarks and gluons, is non-perturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real-time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should allow us to address very challenging problems, ranging from confinement and deconfinement, or chiral symmetry breaking and its restoration at finite baryon density, to color superconductivity and the real-time evolution of heavy-ion collisions, first in simpler model gauge theories and ultimately in QCD.Comment: 27 pages, 6 figures, invited contribution to the "Annalen der Physik" topical issue "Quantum Simulation", guest editors: R. Blatt, I. Bloch, J. I. Cirac, and P. Zolle

Ground and excited states Gamow-Teller strength distributions of iron isotopes and associated capture rates for core-collapse simulations

This paper reports on the microscopic calculation of ground and excited states Gamow-Teller (GT) strength distributions, both in the electron capture and electron decay direction, for $^{54,55,56}$Fe. The associated electron and positron capture rates for these isotopes of iron are also calculated in stellar matter. These calculations were recently introduced and this paper is a follow-up which discusses in detail the GT strength distributions and stellar capture rates of key iron isotopes. The calculations are performed within the framework of the proton-neutron quasiparticle random phase approximation (pn-QRPA) theory. The pn-QRPA theory allows a microscopic \textit{state-by-state} calculation of GT strength functions and stellar capture rates which greatly increases the reliability of the results. For the first time experimental deformation of nuclei are taken into account. In the core of massive stars isotopes of iron, $^{54,55,56}$Fe, are considered to be key players in decreasing the electron-to-baryon ratio ($Y_{e}$) mainly via electron capture on these nuclide. The structure of the presupernova star is altered both by the changes in $Y_{e}$ and the entropy of the core material. Results are encouraging and are compared against measurements (where possible) and other calculations. The calculated electron capture rates are in overall good agreement with the shell model results. During the presupernova evolution of massive stars, from oxygen shell burning stages till around end of convective core silicon burning, the calculated electron capture rates on $^{54}$Fe are around three times bigger than the corresponding shell model rates. The calculated positron capture rates, however, are suppressed by two to five orders of magnitude.Comment: 18 pages, 12 figures, 10 table

M-theory from the superpoint

The “brane scan” classifies consistent Green–Schwarz strings and membranes in terms of the invariant cocycles on super Minkowski spacetimes. The “brane bouquet” generalizes this by consecutively forming the invariant higher central extensions induced by these cocycles, which yields the complete fundamental brane content of string/M-theory, including the D-branes and the M5-brane, as well as the various duality relations between these. This raises the question whether the super Minkowski spacetimes themselves arise as maximal invariant central extensions. Here, we prove that they do. Starting from the simplest possible super Minkowski spacetime, the superpoint, which has no Lorentz structure and no spinorial structure, we give a systematic process of consecutive “maximal invariant central extensions” and show that it discovers the super Minkowski spacetimes that contain superstrings, culminating in the 10- and 11-dimensional super Minkowski spacetimes of string/M-theory and leading directly to the brane bouquet

Irrational behavior in the Brown - von Neuman - Nash dynamics

We present a class of games with a pure strategy being strictly dominated by an- other pure strategy such that the former survives along solutions of the Brown - von Neumann - Nash dynamics from an open set of initial conditions