We derive a bulk-boundary correspondence for three-dimensional (3D) symmetry-protected topological phases with unitary symmetries. The correspondence consists of three equations that relate bulk properties of these phases to properties of their gapped, symmetry-preserving surfaces. Both the bulk and surface data appearing in our correspondence are defined via a procedure in which we gauge the symmetries of the system of interest and then study the braiding statistics of excitations of the resulting gauge theory. The bulk data are defined in terms of the statistics of bulk excitations, while the surface data are defined in terms of the statistics of surface excitations. An appealing property of these data is that it is plausibly complete in the sense that the bulk data uniquely distinguish each 3D symmetry-protected topological phase, while the surface data uniquely distinguish each gapped, symmetric surface. Our correspondence applies to any 3D bosonic symmetryprotected topological phase with finite Abelian unitary symmetry group. It applies to any surface that (1) supports only Abelian anyons and (2) has the property that the anyons are not permuted by the symmetries.

We present an interface for exploring large design spaces as encountered in simulation-based engineering, design of visual effects, and other tasks that require tuning parameters of computationally-intensive simulations and visually evaluating results. The goal is to enable a style of design with simulations that feels as-direct-as-possible so users can concentrate on creative design tasks. The approach integrates forward design via direct manipulation of simulation inputs (e.g., geometric properties, applied forces) in the same visual space with inverse design via “tugging” and reshaping simulation outputs (e.g., scalar fields from finite element analysis (FEA) or computational fluid dynamics (CFD)). The interface includes algorithms for interpreting the intent of users’ drag operations relative to parameterized models, morphing arbitrary scalar fields output from FEA and CFD simulations, and in-place interactive ensemble visualization. The inverse design strategy can be extended to use multi-touch input in combination with an as-rigid-as-possible shape manipulation to support rich visual queries. The potential of this new design approach is confirmed via two applications: medical device engineering of a vacuum-assisted biopsy device and visual effects design using a physically based flame simulation.

We present a field theory description of a quantum phase transition in two spatial dimensions between a U (1) algebraic spin liquid with N flavors of gapless two-component Dirac fermionic spinons and a gapped Z2 spin liquid. This transition is driven by spinon pairing and concomitant Higgsing of the emergent U (1) gauge field. For sufficiently large N we find a quantum critical point with non-Gaussian exponents that is stable against instanton proliferation. We compute critical exponents using either 1/N or expansions, and give estimates of the critical value of N below which the quantum critical point disappears.arXiv:1804.00054v2 [cond-mat.str-el]

We compute in perturbation theory the relation between the B-meson leptonic decay constant FB computed on a lattice by the 1 / m b expansion in the manner of Eichten and the continuum: i.e., the physical value of FB. To that aim we compare the QCD radiative corrections up to order a, of the axial-vector-current correlator for different quark masses with the radiative corrections of the effective operator which replaces the correlator in the I / m b expansion. The latter radiative corrections are computed in the continuum and on a lattice. For this effective operator we recover the anomalous dimension y = 2 already found by Shifman and Voloshin. Our final result is that F, --0. 8 F p 1 , only weakly dependent on lattice spacing and ApcD. I. 1/M EXPANSION AND EFFECTIVE OPERATORLattice calculations lead to rather successful estimates of hadron properties: masses, decay constants such as F,, F K , etc. When considering states which include one or two charmed quarks the situation becomes trickier since present lattices have am, --t and one has no control on corrections of the order am, where a is the lattice spacing and m , the charmed-quark mass. For the b quark the same techniques are out of question since am, >> 1 for any presently realistic lattice. A new approach is necessary. The basic idea was proposed by Eichten. ' It consists of performing a 1 / m b expansion of the heavy-quark propagator. Then any useful Green's function such as correlation functions can be calculated, to some order in l / m b , only from the knowledge of the light-quark propagator and the gluon fields, which in turn can be estimated on a lattice. In principle with this method one can get an answer from the lattice up to corrections of the order 1 / m b a to some power. In fact in what follows we shall stick to the lowest order in 1 / m b a . Numerical calculations on lattice have already been done'32 but they can only give rather loose bounds on FB by lack of statistics.We need also to know the exact relation between the lattice result for FB and its continuum value, and to that aim we must compute the radiative corrections both in the continuum and on the lattice. However, some care is needed since the l / m , expansion breaks down for the frequencies of gluon fields which are not small compared t o m , .T o state more precisely the problem, let us first recall what happens in the case of F , (Refs. 3 and 4). One computes the correlation function of two axial-vector currents. These have a vanishing anomalous dimension due to partial conservation of the axial-vector current. The local axial-vector current on the lattice has also no anomalous dimension but it differs from the corresponding operator in the continuum by some finite radiative corrections. These corrections come from the high frequencies which differ on a lattice and in the continuum.Let us now consider the current 6yPySq. As in the case of F , the correlation function between two such currents leads to F B . As we have argued before, the radiative corrections in the continuum a...