Semiclassical approximation in Batalin-Vilkovisky formalism

The geometry of supermanifolds provided with $Q$-structure (i.e. with odd vector field $Q$ satisfying $\{ Q,Q\} =0$), $P$-structure (odd symplectic structure ) and $S$-structure (volume element) or with various combinations of these structures is studied. The results are applied to the analysis of Batalin-Vilkovisky approach to the quantization of gauge theories. In particular the semiclassical approximation in this approach is expressed in terms of Reidemeister torsion.Comment: 27 page

Geometry of Batalin-Vilkovisky quantization

The present paper is devoted to the study of geometry of Batalin-Vilkovisky quantization procedure. The main mathematical objects under consideration are P-manifolds and SP-manifolds (supermanifolds provided with an odd symplectic structure and, in the case of SP-manifolds, with a volume element). The Batalin-Vilkovisky procedure leads to consideration of integrals of the superharmonic functions over Lagrangian submanifolds. The choice of Lagrangian submanifold can be interpreted as a choice of gauge condition; Batalin and Vilkovisky proved that in some sense their procedure is gauge independent. We prove much more general theorem of the same kind. This theorem leads to a conjecture that one can modify the quantization procedure in such a way as to avoid the use of the notion of Lagrangian submanifold. In the next paper we will show that this is really so at least in the semiclassical approximation. Namely the physical quantities can be expressed as integrals over some set of critical points of solution S to the master equation with the integrand expressed in terms of Reidemeister torsion. This leads to a simplification of quantization procedure and to the possibility to get rigorous results also in the infinite-dimensional case. The present paper contains also a compete classification of P-manifolds and SP-manifolds. The classification is interesting by itself, but in this paper it plays also a role of an important tool in the proof of other results.Comment: 13 page

Solving the noncommutative Batalin-Vilkovisky equation

I show that a summation over ribbon graphs with legs gives the construction of the solutions to the noncommutative Batalin-Vilkovisky equation, including the equivariant version. This generalizes the known construction of A-infinity algebra via summation over ribbon trees. These solutions give naturally the supersymmetric matrix action functionals, which are the gl(N)-equivariantly closed differential forms on the matrix spaces, which were introduced in one of my previous papers "Noncommmutative Batalin-Vilkovisky geometry and Matrix integrals" (arXiv:0912.5484, electronic CNRS preprint hal-00102085(28/09/2006)).Comment: 17 pages, electronic CNRS preprint hal-00464794 (17/03/2010

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.

Gauge-fixing, semiclassical approximation and potentials for graded Chern-Simons theories

We perform the Batalin-Vilkovisky analysis of gauge-fixing for graded Chern-Simons theories. Upon constructing an appropriate gauge-fixing fermion, we implement a Landau-type constraint, finding a simple form of the gauge-fixed action. This allows us to extract the associated Feynman rules taking into account the role of ghosts and antighosts. Our gauge-fixing procedure allows for zero-modes, hence is not limited to the acyclic case. We also discuss the semiclassical approximation and the effective potential for massless modes, thereby justifying some of our previous constructions in the Batalin-Vilkovisky approach.Comment: 46 pages, 4 figure

Therapeutic efficacy of anti-MMP9 antibody in combination with nab-paclitaxel-based chemotherapy in pre-clinical models of pancreatic cancer

Matrix metalloproteinase 9 (MMP9) is involved in the proteolysis of extracellular proteins and plays a critical role in pancreatic ductal adenocarcinoma (PDAC) progression, invasion and metastasis. The therapeutic potential of an anti-MMP9 antibody (αMMP9) was evaluated in combination with nab-paclitaxel (NPT)-based standard cytotoxic therapy in pre-clinical models of PDAC. Tumour progression and survival studies were performed in NOD/SCID mice. The mechanistic evaluation involved RNA-Seq, Luminex, IHC and Immunoblot analyses of tumour samples. Median animal survival compared to controls was significantly increased after 2-week therapy with NPT (59%), Gem (29%) and NPT+Gem (76%). Addition of αMMP9 antibody exhibited further extension in survival: NPT+αMMP9 (76%), Gem+αMMP9 (47%) and NPT+Gem+αMMP9 (94%). Six-week maintenance therapy revealed that median animal survival was significantly increased after NPT+Gem (186%) and further improved by the addition of αMMP9 antibody (218%). Qualitative assessment of mice exhibited that αMMP9 therapy led to a reduction in jaundice, bloody ascites and metastatic burden. Anti-MMP9 antibody increased the levels of tumour-associated IL-28 (1.5-fold) and decreased stromal markers (collagen I, αSMA) and the EMT marker vimentin. Subcutaneous tumours revealed low but detectable levels of MMP9 in all therapy groups but no difference in MMP9 expression. Anti-MMP9 antibody monotherapy resulted in more gene expression changes in the mouse stroma compared to the human tumour compartment. These findings suggest that anti-MMP9 antibody can exert specific stroma-directed effects that could be exploited in combination with currently used cytotoxics to improve clinical PDAC therapy

Comment on the Surface Exponential for Tensor Fields

Starting from essentially commutative exponential map $E(B|I)$ for generic tensor-valued 2-forms $B$, introduced in \cite{Akh} as direct generalization of the ordinary non-commutative $P$-exponent for 1-forms with values in matrices (i.e. in tensors of rank 2), we suggest a non-trivial but multi-parametric exponential ${\cal E}(B|I|t_\gamma)$, which can serve as an interesting multi-directional evolution operator in the case of higher ranks. To emphasize the most important aspects of the story, construction is restricted to backgrounds $I_{ijk}$, associated with the structure constants of {\it commutative} associative algebras, what makes it unsensitive to topology of the 2d surface. Boundary effects are also eliminated (straightfoward generalization is needed to incorporate them).Comment: 6 page

Kinematic and morphological modeling of the bipolar nebula Sa2-237

We present [OIII]500.7nm and Halpha+[NII] images and long-slit, high resolution echelle spectra in the same spectral regions of Sa2--237, a possible bipolar planetary nebula. The image shows a bipolar nebula of about 34" extent, with a narrow waist, and showing strong point symmetry about the central object, indicating it's likely binary nature. The long slit spectra were taken over the long axis of the nebula, and show a distinct ``eight'' shaped pattern in the velocity--space plot, and a maximum projected outflow velocity of V=106km/s, both typical of expanding bipolar planetary nebulae. By model fitting the shape and spectrum of the nebula simultaneously, we derive the inclination of the long axis to be 70 degrees, and the maximum space velocity of expansion to be 308 km/s. Due to asymmetries in the velocities we adopt a new value for the system's heliocentric radial velocity of -30km/s. We use the IRAS and 21cm radio fluxes, the energy distribution, and the projected size of Sa2-237 to estimate it's distance to be 2.1+-0.37kpc. At this distance Sa2-237 has a luminosity of 340 Lsun, a size of 0.37pc, and -- assuming constant expansion velocity -- a nebular age of 624 years. The above radial velocity and distance place Sa2--237 in the disk of the Galaxy at z=255pc, albeit with somewhat peculiar kinematics.Comment: 10pp, 4 fig

A Note on Marginally Stable Bound States in Type II String Theory

Spectrum of elementary string states in type II string theory contains ultra-short multiplets that are marginally stable. $U$-duality transformation converts these states into bound states at threshold of $p$-branes carrying Ramond-Ramond charges, and wrapped around $p$-cycles of a torus. We propose a test for the existence of these marginally stable bound states. Using the recent results of Polchinski and of Witten, we argue that the spectrum of bound states of $p$-branes is in agreement with the prediction of $U$-duality.Comment: LaTeX file, 6 page

XMM-Newton observations of the Perseus Cluster I: The temperature and surface brightness structure

We present preliminary results of the XMM-Newton 50 ksec observation of the Perseus cluster. The global east/west asymmetry of the gas temperature and surface brightness distributions, approximately aligned with the chain of bright galaxies, suggests an ongoing merger, although the modest degree of the observed asymmetry certainly excludes a major merger interpretation. The chain of galaxies probably traces the filament along which accretion has started some time ago and is continuing at the present time. A cold and dense (low entropy) cluster core like Perseus is probably well "protected" against the penetration of the gas of infalling groups and poor clusters whereas in non-cooling core clusters like Coma and A1367, infalling subclusters can penetrate deeply into the core region. In Perseus, gas associated with infalling groups may be stripped completely at the outskirts of the main cluster and only compression waves (shocks) may reach the central regions. We argue that the passage of such a wave(s) can qualitatively explain the overall horseshoe shaped appearance of the gas temperature map (the hot horseshoe surrounds the colder, low entropy core) as well as other features of the Perseus cluster core. As compression waves traverse the cluster core, they can induce oscillatory motion of the cluster gas which can generate multiple sharp "edges", on opposite sides or the central galaxy. Gas motions induced by mergers may be a natural way to explain the high frequency of "edges" seen in clusters with cooling cores.Comment: 16 pages, 14 figures, submitted to Ap