On finite volume effects in the chiral extrapolation of baryon masses

We perform an analysis of the QCD lattice data on the baryon octet and decuplet masses based on the relativistic chiral Lagrangian. The baryon self energies are computed in a finite volume at next-to-next-to-next-to leading order (N$^3$LO), where the dependence on the physical meson and baryon masses is kept. The number of free parameters is reduced significantly down to 12 by relying on large-$N_c$ sum rules. Altogether we describe accurately more than 220 data points from six different lattice groups, BMW, PACS-CS, HSC, LHPC, QCDSF-UKQCD and NPLQCD. Values for all counter terms relevant at N$^3$LO are predicted. In particular we extract a pion-nucleon sigma term of 39$_{-1}^{+2}$ MeV and a strangeness sigma term of the nucleon of $\sigma_{sN} = 84^{+ 28}_{-\;4}$ MeV. The flavour SU(3) chiral limit of the baryon octet and decuplet masses is determined with $(802 \pm 4)$ MeV and $(1103 \pm 6)$ MeV. Detailed predictions for the baryon masses as currently evaluated by the ETM lattice QCD group are made.Comment: 44 pages, 10 figures and 6 tables - the revised manuscript contains the results of additional fits at the N^2LO level - 4 additional figures show the size of finite volume corrections for each lattice point - more technical details on the evaluation of finite volume effects are give

Abelian Duality

We show that on three-dimensional Riemannian manifolds without boundaries and with trivial first real de Rham cohomology group (and in no other dimensions) scalar field theory and Maxwell theory are equivalent: the ratio of the partition functions is given by the Ray-Singer torsion of the manifold. On the level of interaction with external currents, the equivalence persists provided there is a fixed relation between the charges and the currents.Comment: 11 pages, LaTeX, no figures, a reference added, submitted to Phys. Rev.

An optimal algorithm for the on-line closest-pair problem

We give an algorithm that computes the closest pair in a set of $n$ points in $k$-dimensional space on-line, in $O(n \log n)$ ime. The algorithm only uses algebraic functions and, therefore, is optimal. The algorithm maintains a hierarchical subdivision of $k$-space into hyperrectangles, which is stored in a binary tree. Centroids are used to maintain a balanced decomposition of this tree

Antarctic meteorite descriptions, 1980

Specimens found in the Alan Hills area include 361 ordinary chondrites, 4 carbonaceous chondrites, 6 achondrites, and 2 irons. Thirteen specimens measured over 11 cm in diameter and 69 between 5 to 10 cm in diameter are reported. The remainder of the finds were small, and many were paired. One of the irons was estimated to weigh about 20 kilograms

Polarizations and Nullcone of Representations of Reductive Groups

The paper starts with the following simple observation. Let V be a representation of a reductive group G, and let f_1,f_2,...,f_n be homogeneous invariant functions. Then the polarizations of f_1,f_2,...,f_n define the nullcone of k 0} h(t) x = 0 for all x in L. This is then applied to many examples. A surprising result is about the group SL(2,C) where almost all representations V have the property that all linear subspaces of the nullcone are annihilated. Again, this has interesting applications to the invariants on several copies. Another result concerns the n-qubits which appear in quantum computing. This is the representation of a product of n copies of $SL_2$ on the n-fold tensor product C^2 otimes C^2 otimes ... otimes C^2. Here we show just the opposite, namely that the polarizations never define the nullcone of several copies if n <= 3. (An earlier version of this paper, distributed in 2002, was split into two parts; the first part with the title ``On the nullcone of representations of reductive groups'' is published in Pacific J. Math. {bf 224} (2006), 119--140.

M-Theory on (K3 X S^1)/Z_2

We analyze $M$-theory compactified on $(K3\times S^1)/Z_2$ where the $Z_2$ changes the sign of the three form gauge field, acts on $S^1$ as a parity transformation and on K3 as an involution with eight fixed points preserving SU(2) holonomy. At a generic point in the moduli space the resulting theory has as its low energy limit N=1 supergravity theory in six dimensions with eight vector, nine tensor and twenty hypermultiplets. The gauge symmetry can be enhanced (e.g. to $E_8$) at special points in the moduli space. At other special points in the moduli space tensionless strings appear in the theory.Comment: LaTeX file, 11 page

Preparing projected entangled pair states on a quantum computer

We present a quantum algorithm to prepare injective PEPS on a quantum computer, a class of open tensor networks representing quantum states. The run-time of our algorithm scales polynomially with the inverse of the minimum condition number of the PEPS projectors and, essentially, with the inverse of the spectral gap of the PEPS' parent Hamiltonian.Comment: 5 pages, 1 figure. To be published in Physical Review Letters. Removed heuristics, refined run-time boun