The 3d Stress-Tensor Bootstrap

We study the conformal bootstrap for 4-point functions of stress tensors in parity-preserving 3d CFTs. To set up the bootstrap equations, we analyze the constraints of conformal symmetry, permutation symmetry, and conservation on the stress-tensor 4-point function and identify a non-redundant set of crossing equations. Studying these equations numerically using semidefinite optimization, we compute bounds on the central charge as a function of the independent coefficient in the stress-tensor 3-point function. With no additional assumptions, these bounds numerically reproduce the conformal collider bounds and give a general lower bound on the central charge. We also study the effect of gaps in the scalar, spin-2, and spin-4 spectra on the central charge bound. We find general upper bounds on these gaps as well as tighter restrictions on the stress-tensor 3-point function coefficients for theories with moderate gaps. When the gap for the leading scalar or spin-2 operator is sufficiently large to exclude large N theories, we also obtain upper bounds on the central charge, thus finding compact allowed regions. Finally, assuming the known low-lying spectrum and central charge of the critical 3d Ising model, we determine its stress-tensor 3-point function and derive a bound on its leading parity-odd scalar.Comment: 51 pages, 17 figure

Heavy-particle formalism with Foldy-Wouthuysen representation

Utilizing the Foldy-Wouthuysen representation, we use a bottom-up approach to construct heavy-baryon Lagrangian terms, without employing a relativistic Lagrangian as the starting point. The couplings obtained this way feature a straightforward $1/m$ expansion, which ensures Lorentz invariance order by order in effective field theories. We illustrate possible applications with two examples in the context of chiral effective field theory: the pion-nucleon coupling, which reproduces the results in the literature, and the pion-nucleon-delta coupling, which does not employ the Rarita-Schwinger field for describing the delta isobar, and hence does not invoke any spurious degrees of freedom. In particular, we point out that one of the subleading $\pi N \Delta$ couplings used in the literature is, in fact, redundant, and discuss the implications of this. We also show that this redundant term should be dropped if one wants to use low-energy constants fitted from $\pi N$ scattering in calculations of $NN\to NN\pi$ reactions.Comment: 28 pages, 2 figures, RevTeX4, appendix added, version published in Phys. Rev.

Sparse Graph Codes for Quantum Error-Correction

We present sparse graph codes appropriate for use in quantum error-correction. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based on sparse graphs. Second, sparse graph codes keep the number of quantum interactions associated with the quantum error correction process small: a constant number per quantum bit, independent of the blocklength. Third, sparse graph codes often offer great flexibility with respect to blocklength and rate. We believe some of the codes we present are unsurpassed by previously published quantum error-correcting codes.Comment: Version 7.3e: 42 pages. Extended version, Feb 2004. A shortened version was resubmitted to IEEE Transactions on Information Theory Jan 20, 200

Standard interface definition for avionics data bus systems

Data bus for avionics system of space shuttle, noting functions of interface unit, error detection and recovery, redundancy, and bus control philosoph

Fermionic projected entangled-pair states and topological phases

We study fermionic matrix product operator algebras and identify the associated algebraic data. Using this algebraic data we construct fermionic tensor network states in two dimensions that have non-trivial symmetry-protected or intrinsic topological order. The tensor network states allow us to relate physical properties of the topological phases to the underlying algebraic data. We illustrate this by calculating defect properties and modular matrices of supercohomology phases. Our formalism also captures Majorana defects as we show explicitly for a class of $\mathbb{Z}_2$ symmetry-protected and intrinsic topological phases. The tensor networks states presented here are well-suited for numerical applications and hence open up new possibilities for studying interacting fermionic topological phases.Comment: Published versio

Adaptive voting computer system

A computer system is reported that uses adaptive voting to tolerate failures and operates in a fail-operational, fail-safe manner. Each of four computers is individually connected to one of four external input/output (I/O) busses which interface with external subsystems. Each computer is connected to receive input data and commands from the other three computers and to furnish output data commands to the other three computers. An adaptive control apparatus including a voter-comparator-switch (VCS) is provided for each computer to receive signals from each of the computers and permits adaptive voting among the computers to permit the fail-operational, fail-safe operation

Equivariant semidefinite lifts and sum-of-squares hierarchies

A central question in optimization is to maximize (or minimize) a linear function over a given polytope P. To solve such a problem in practice one needs a concise description of the polytope P. In this paper we are interested in representations of P using the positive semidefinite cone: a positive semidefinite lift (psd lift) of a polytope P is a representation of P as the projection of an affine slice of the positive semidefinite cone $\mathbf{S}^d_+$. Such a representation allows linear optimization problems over P to be written as semidefinite programs of size d. Such representations can be beneficial in practice when d is much smaller than the number of facets of the polytope P. In this paper we are concerned with so-called equivariant psd lifts (also known as symmetric psd lifts) which respect the symmetries of the polytope P. We present a representation-theoretic framework to study equivariant psd lifts of a certain class of symmetric polytopes known as orbitopes. Our main result is a structure theorem where we show that any equivariant psd lift of size d of an orbitope is of sum-of-squares type where the functions in the sum-of-squares decomposition come from an invariant subspace of dimension smaller than d^3. We use this framework to study two well-known families of polytopes, namely the parity polytope and the cut polytope, and we prove exponential lower bounds for equivariant psd lifts of these polytopes.Comment: v2: 30 pages, Minor changes in presentation; v3: 29 pages, New structure theorem for general orbitopes + changes in presentatio