On complexes related with calculus of variations

We consider the variational complex on infinite jet space and the complex of variational derivatives for Lagrangians of multidimensional paths and study relations between them. The discussion of the variational (bi)complex is set up in terms of a flat connection in the jet bundle. We extend it to supercase using a particular new class of forms. We establish relation of the complex of variational derivatives and the variational complex. Certain calculus of Lagrangians of multidimensional paths is developed. It is shown how covariant Lagrangians of higher order can be used to represent characteristic classes.Comment: LaTeX2e, 36 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

Duality Symmetry in the Schwarz-Sen Model

The continuous extension of the discrete duality symmetry of the Schwarz-Sen model is studied. The corresponding infinitesimal generator $Q$ turns out to be local, gauge invariant and metric independent. Furthermore, $Q$ commutes with all the conformal group generators. We also show that $Q$ is equivalent to the non---local duality transformation generator found in the Hamiltonian formulation of Maxwell theory. We next consider the Batalin--Fradkin-Vilkovisky formalism for the Maxwell theory and demonstrate that requiring a local duality transformation lead us to the Schwarz--Sen formulation. The partition functions are shown to be the same which implies the quantum equivalence of the two approaches.Comment: 10 pages, latex, small changes, final version to appear in Phys. Rev.

On Duality in the Born-Infeld Theory

The $SL(2,R)$ duality symmetric action for the Born-Infeld theory in terms of two potentials, coupled with non-trivial backgroud fields in four dimensions is established. This construction is carried out in detail by analysing the hamiltonian structure of the Born-Infeld theory. The equivalence with the usual Born-Infeld theory is shown.Comment: revtex, 4 page

Dense Ionized and Neutral Gas Surrounding Sgr A*

We present high resolution H41a hydrogen recombination line observations of the 1.2' (3 pc) region surrounding Sgr A* at 92 GHz using the OVRO Millimeter Array with an angular resolution of 7" x 3" and velocity resolution of 13 km/s. New observations of H31a, H35a, H41a, and H44a lines were obtained using the NRAO 12-m telescope, and their relative line strengths are interpreted in terms of various emission mechanisms. These are the most extensive and most sensitive observations of recombination line to date. Observations of HCO+ (1 - 0) transition at 89 GHz are also obtained simultaneously with a 40% improved angular resolution and 4-15 times improved sensitivity over previous observations, and the distribution and kinematics of the dense molecular gas in the circumnuclear disk (CND) are mapped and compared with those of the ionized gas. The line brightness ratios of the hydrogen recombination lines are consistent with purely spontaneous emission from 7000 K gas with n_e = 20,000 cm$^{-3}$ near LTE condition. A virial analysis suggests that the most prominent molecular gas clumps in the CND have mean densities of 10^7 cm^{-3}, sufficient to withstand the tidal shear in the Galactic Center region. Therefore, these clumps may survive over several dynamical times, and the CND may be a dynamically stable structure. We estimate a total gas mass of 3 x 10^5 solar mass for the CND. \Comment: 34 pages including 11 figures (4 jpgs), Latex, uses aastex. The full pdf format file including high resolution figures is available at http://www.astro.umass.edu/~myun/papers/SgrA.pdf . To appear in the 20 November 2004 (V616) issue of the Astrophysical Journa

Non Abelian TQFT and scattering of self dual field configuration

A non-abelian topological quantum field theory describing the scattering of self-dual field configurations over topologically non-trivial Riemann surfaces, arising from the reduction of 4-dim self-dual Yang-Mills fields, is introduced. It is shown that the phase space of the theory can be exactly quantized in terms of the space of holomorphic structures over stable vector bundles of degree zero over Riemann surfaces. The Dirac monopoles are particular static solutions of the field equations. Its relation to topological gravity is discussed.Comment: 13 pages, Late

Poincare Invariance of a Quantized Duality Symmetric Theory

The noncovariant duality symmetric action put forward by Schwarz-Sen is quantized by means of the Dirac bracket quantization procedure. The resulting quantum theory is shown to be, nevertheless, relativistically invariant

Lattice QCD and the Schwarz alternating procedure

A numerical simulation algorithm for lattice QCD is described, in which the short- and long-distance effects of the sea quarks are treated separately. The algorithm can be regarded, to some extent, as an implementation at the quantum level of the classical Schwarz alternating procedure for the solution of elliptic partial differential equations. No numerical tests are reported here, but theoretical arguments suggest that the algorithm should work well also at small quark masses.Comment: Plain TeX source, 20 pages, figures include

Macrophage Polarization is Deregulated in Haemophilia

Macrophages make important contributions to inflammation and wound healing. We show here that macrophage polarization is deregulated in haemophilia in response to macrophage colony-stimulating factor (M-CSF) and partially in response to granulocyte-macrophage colony-stimulating factor (GM-CSF). As a result, haemophilia macrophages exhibit a specific impairment of M-CSF-mediated functions involved in wound healing such as clot invasion and phagocytosis. Haemophilia monocytes express reduced amounts of the receptors for M-CSF and GM-CSF, which correlates with a failure to express tumour necrosis factor α (TNFα) and CD163 in M-CSF-treated haemophilia macrophages and reduced expression of TNFα and CD206 after treatment with GM-CSF. Protein expression in response to M-CSF was regained with respect to CD163 and CD206 after embedding haemophilia monocytes in clotted plasma suggesting that a functioning coagulation system has positive effects on macrophage M2 polarization. Mimicking the functional deficits of haemophilia macrophages in normal macrophages was possible by adding leptin, which we found to be elevated in the blood of haemophilia patients, to a monocyte cell line. The increase of leptin occurred in conjunction with C-reactive protein in a body mass index-controlled cohort suggesting that haemophilia patients harbour chronic low-grade inflammation. Together, our data indicate that impaired clotting in haemophilia patients leads to increased inflammation and a deregulation in macrophage differentiation, which may explain the commonly observed deficits in wound healing and tissue regeneration

Classification of N=6 superconformal theories of ABJM type

Studying the supersymmetry enhancement mechanism of Aharony, Bergman, Jafferis and Maldacena, we find a simple condition on the gauge group generators for the matter fields. We analyze all possible compact Lie groups and their representations. The only allowed gauge groups leading to the manifest N=6 supersymmetry are, up to discrete quotients, SU(n) x U(1), Sp(n) x U(1), SU(n) x SU(n), and SU(n) x SU(m) x U(1) with possibly additional U(1)'s. Matter representations are restricted to be the (bi)fundamentals. As a byproduct we obtain another proof of the complete classification of the three algebras considered by Bagger and Lambert.Comment: 18 page