Sundance Bilson-Thompson

Quantum gravity and the standard model

We show that a class of background-independent models of quantum spacetime have local excitations that can be mapped to the first-generation fermions of the standard model of particle physics. These states propagate coherently as they can be shown to be noiseless subsystems of the microscopic quantum dynamics (Kribs and Markopoulou 2005 Preprint gr-qc/0510052, Markopoulou and Poulin unpublished). These are identified in terms of certain patterns of braiding of graphs, thus giving a quantum gravitational foundation for the topological preon model proposed by Bilson-Thompson (2005 Preprint hep-ph/0503213). These results apply to a large class of theories in which the Hilbert space has a basis of states given by ribbon graphs embedded in a three-dimensional manifold up to diffeomorphisms, and the dynamics is given by local moves on the graphs, such as arise in the representation theory of quantum groups. For such models, matter appears to be already included in the microscopic kinematics and dynamics.

Hadron masses from novel fat link fermion actions

The hadron mass spectrum is calculated in lattice QCD using a novel fat-link clover fermion action in which only the irrelevant operators in the fermion action are constructed using smeared links. The simulations are performed on a 16{sup 3} x 32 lattice with a lattice spacing of a=0.125 fm. We compare actions with n=4 and 12 smearing sweeps with a smearing fraction of 0.7. The n=4 Fat-Link Irrelevant Clover (FLIC) action provides scaling which is superior to mean-field improvement, and offers advantages over nonperturbative 0(a) improvement, including a reduced exceptional configuration problem.

Excited Baryons in Lattice QCD

We present first results for the masses of positive and negative parity excited baryons calculated in lattice QCD using an O(a^2)-improved gluon action and a fat-link irrelevant clover (FLIC) fermion action in which only the irrelevant operators are constructed with APE-smeared links. The results are in agreement with earlier calculations of N^* resonances using improved actions and exhibit a clear mass splitting between the nucleon and its chiral partner. An correlation matrix analysis reveals two low-lying J^P=(1/2)^- states with a small mass splitting. The study of different Lambda interpolating fields suggests a similar splitting between the lowest two Lambda1/2^- octet states. However, the empirical mass suppression of the Lambda^*(1405) is not evident in these quenched QCD simulations, suggesting a potentially important role for the meson cloud of the Lambda^*(1405) and/or a need for more exotic interpolating fields.

Highly improved lattice field-strength tensor

Abstract We derive an O (a 4 ) -improved lattice version of the continuum field-strength tensor. Discretization errors are reduced via the combination of several clover terms of various sizes, complemented by tadpole improvement. The resulting improved field-strength tensor is used to construct O (a 4 ) -improved topological charge and action operators. As a test of our improved field-strength tensor, we compare the values attained by these operators as we cool several configurations to self-duality with a previously defined highly improved action and assess the relative scale of the remaining discretization errors. We demonstrate accuracy to better than one part in 10,000.

Novel Fat-Link Fermion Actions

The hadron mass spectrum is calculated in lattice QCD using a novel fat-link clover fermion action in which only the irrelevant operators of the fermion action are constructed using smeared links. The simulations are performed on a 16^3 X 32 lattice with a lattice spacing of a=0.125 fm. We compare actions with n=4 and 12 smearing sweeps with a smearing fraction of 0.7. The n=4 Fat Link Irrelevant Clover (FLIC) action provides scaling which is superior to mean-field improvement, and offers advantages over nonperturbative O(a) improvement.The hadron mass spectrum is calculated in lattice QCD using a novel fat-link clover fermion action in which only the irrelevant operators in the fermion action are constructed using smeared links. The simulations are performed on a 16{sup 3} x 32 lattice with a lattice spacing of a=0.125 fm. We compare actions with n=4 and 12 smearing sweeps with a smearing fraction of 0.7. The n=4 Fat-Link Irrelevant Clover (FLIC) action provides scaling which is superior to mean-field improvement, and offers advantages over nonperturbative 0(a) improvement.

Cooling for instantons and the wrath of Nahm

The dynamics of instantons and anti-instantons in lattice QCD can be studied by analysing the action and topological charge of configurations as they approach a self-dual or anti-self-dual state, i.e. a state in which S/S0 = |Q|. We use cooling to reveal the semi-classical structure of the configurations we study. Improved actions which eliminate discretisation errors up to and including O(a4) are used to stabilise instantons as we cool for several thousand sweeps. An analogously improved lattice version of the continuum field-strength tensor is used to construct a topological charge free from O(a4) discretisation errors. Values of the action and topological charge obtained with these improved operators approach mutually-consistent integer values to within a few parts in 104 after several hundred cooling sweeps. Analysis of configurations with |Q| ≈ 1 and |Q| ≈ 2 supports the hypothesis that a self-dual |Q| = 1 configuration cannot exist on the 4-torus.

Numerical study of the lattice index theorem using improved cooling and overlap fermions

J. B. Zhang, S. O. Bilson-Thompson, F. D. R. Bonnet, D. B. Leinweber, A. G. Williams, and J. M. Zanotti

LQG for the Bewildered

We present a pedagogical introduction to the notions underlying the connec- tion formulation of General Relativity - Loop Quantum Gravity (LQG) - with an emphasis on the physical aspects of the framework. We begin by reviewing General Relativity and Quantum Field Theory, to emphasise the similarities between them which establish a foun- dation upon which to build a theory of quantum gravity. We then explain, in a concise and clear manner, the steps leading from the Einstein-Hilbert action for gravity to the construction of the quantum states of geometry, known as spin-networks, which provide the basis for the kinematical Hilbert space of quantum general relativity. Along the way we introduce the various associated concepts of tetrads, spin-connection and holonomies which are a pre-requisite for understanding the LQG formalism. Having provided a min- imal introduction to the LQG framework, we discuss its applications to the problems of black hole entropy and of quantum cosmology. A list of the most common criticisms of LQG is presented, which are then tackled one by one in order to convince the reader of the physical viability of the theory. An extensive set of appendices provide accessible introductions to several key notions such as the Peter-Weyl theorem, duality of dierential forms and Regge calculus, among others. The presentation is aimed at graduate students and researchers who have some familiarity with the tools of quantum mechanics and

Comparison of |Q| = 1 and |Q| = 2 Gauge-Field Configurations on the Lattice Four-Torus

Abstract It is known that exactly self-dual gauge-field configurations with topological charge |Q|=1 cannot exist on the untwisted continuum four-torus. We explore the manifestation of this remarkable fact on the lattice four-torus for SU(3) using advanced techniques for controlling lattice discretization errors, extending earlier work of De Forcrand et al. for SU(2). We identify three distinct signals for the instability of |Q|=1 configurations, and show that these signals manifest themselves early in the cooling process, long before the would-be instanton has shrunk to a size comparable to the lattice discretization threshold. These signals do not appear for the individual instantons which make up our |Q|=2 configurations. This indicates that these signals reflect the truly global nature of the instability, rather than the local discretization effects which cause the eventual disappearance of the would-be single instanton. Monte-Carlo generated SU(3) gauge-field configurations are cooled to the self-dual limit using an O (a 4 ) -improved gauge action chosen to have small but positive O (a 6 ) errors. This choice prevents lattice discretization errors from destroying instantons provided their size exceeds the dislocation threshold of the cooling algorithm. Lattice discretization errors are evaluated by comparing the O (a 4 ) -improved gauge-field action with an O (a 4 ) -improved action constructed from the square of an O (a 4 ) -improved lattice field-strength tensor, thus having different O (a 6 ) discretization errors. The number of action-density peaks, the instanton size, and the topological charge of configurations is monitored. We observe a fluctuation in the total topological charge of |Q|=1 configurations, and demonstrate that the onset of this unusual behavior corresponds with the disappearance of multiple-peaks in the action density. At the same time discretization errors are minimal.

Baryon Resonances from a Novel Fat-Link Fermion Action

We present first results for masses of positive and negative parity excited baryons in lattice QCD using an O(a2) improved gluon action and a Fat Link Irrelevant Clover (FLIC) fermion action in which only the irrelevant operators are constructed with fat links. The results are in agreement with earlier calculations of N∗ resonances using improved actions and exhibit a clear mass splitting between the nucleon and its chiral partner, even for the Wilson fermion action. The results also indicate a splitting between the lowest JP = 12− states for the two standard nucleon interpolating fields.We present first results for masses of positive and negative parity excited baryons in lattice QCD using an O(a^2) improved gluon action and a Fat Link Irrelevant Clover (FLIC) fermion action in which only the irrelevant operators are constructed with fat links. The results are in agreement with earlier calculations of N^* resonances using improved actions and exhibit a clear mass splitting between the nucleon and its chiral partner, even for the Wilson fermion action. The results also indicate a splitting between the lowest J^P = 1/2^- states for the two standard nucleon interpolating fields.