AKSZ construction from reduction data

We discuss a general procedure to encode the reduction of the target space geometry into AKSZ sigma models. This is done by considering the AKSZ construction with target the BFV model for constrained graded symplectic manifolds. We investigate the relation between this sigma model and the one with the reduced structure. We also discuss several examples in dimension two and three when the symmetries come from Lie group actions and systematically recover models already proposed in the literature.Comment: 42 page

Geometry and Dynamics of a Coupled 4D-2D Quantum Field Theory

Geometric and dynamical aspects of a coupled 4D-2D interacting quantum field theory - the gauged nonAbelian vortex - are investigated. The fluctuations of the internal 2D nonAbelian vortex zeromodes excite the massless 4D Yang-Mills modes and in general give rise to divergent energies. This means that the well-known 2D CP(N-1) zeromodes associated with a nonAbelian vortex become nonnormalizable. Moreover, all sorts of global, topological 4D effects such as the nonAbelian Aharonov-Bohm effect come into play. These topological global features and the dynamical properties associated with the fluctuation of the 2D vortex moduli modes are intimately correlated, as shown concretely here in a U(1) x SU(N) x SU(N) model with scalar fields in a bifundamental representation of the two SU(N) factor gauge groups.Comment: Latex, 39 pages, 5 figure

The partition bundle of type A_{N-1} (2, 0) theory

Six-dimensional (2, 0) theory can be defined on a large class of six-manifolds endowed with some additional topological and geometric data (i.e. an orientation, a spin structure, a conformal structure, and an R-symmetry bundle with connection). We discuss the nature of the object that generalizes the partition function of a more conventional quantum theory. This object takes its values in a certain complex vector space, which fits together into the total space of a complex vector bundle (the `partition bundle') as the data on the six-manifold is varied in its infinite-dimensional parameter space. In this context, an important role is played by the middle-dimensional intermediate Jacobian of the six-manifold endowed with some additional data (i.e. a symplectic structure, a quadratic form, and a complex structure). We define a certain hermitian vector bundle over this finite-dimensional parameter space. The partition bundle is then given by the pullback of the latter bundle by the map from the parameter space related to the six-manifold to the parameter space related to the intermediate Jacobian.Comment: 15 pages. Minor changes, added reference

Effective Batalin--Vilkovisky theories, equivariant configuration spaces and cyclic chains

Kontsevich's formality theorem states that the differential graded Lie algebra of multidifferential operators on a manifold M is L-infinity-quasi-isomorphic to its cohomology. The construction of the L-infinity map is given in terms of integrals of differential forms on configuration spaces of points in the upper half-plane. Here we consider configuration spaces of points in the disk and work equivariantly with respect to the rotation group. This leads to considering the differential graded Lie algebra of multivector fields endowed with a divergence operator. In the case of R^d with standard volume form, we obtain an L-infinity morphism of modules over this differential graded Lie algebra from cyclic chains of the algebra of functions to multivector fields. As a first application we give a construction of traces on algebras of functions with star-products associated with unimodular Poisson structures. The construction is based on the Batalin--Vilkovisky quantization of the Poisson sigma model on the disk and in particular on the treatment of its zero modes.Comment: 27 page

Supersymmetric Deformations of Maximally Supersymmetric Gauge Theories

We study supersymmetric and super Poincar\'e invariant deformations of ten-dimensional super Yang-Mills theory and of its dimensional reductions. We describe all infinitesimal super Poincar\'e invariant deformations of equations of motion of ten-dimensional super Yang-Mills theory and its reduction to a point; we discuss the extension of them to formal deformations. Our methods are based on homological algebra, in particular, on the theory of L-infinity and A-infinity algebras. The exposition of this theory as well as of some basic facts about Lie algebra homology and Hochschild homology is given in appendices.Comment: New results added. 111 page

Influences of salinity on the physiology and distribution of the Arctic coralline algae, Lithothamnion glaciale (Corallinales, Rhodophyta)

In Greenland, free-living red coralline algae contribute to and dominate marine habitats along the coastline. Lithothamnion glaciale dominates coralline algae beds in many regions of the Arctic, but never in Godthåbsfjord, Greenland, where Clathromorphum sp. is dominant. To investigate environmental impacts on coralline algae distribution, calcification and primary productivity were measured in situ during summers of 2015 and 2016, and annual patterns of productivity in L. glaciale were monitored in laboratory-based mesocosm experiments where temperature and salinity were manipulated to mimic high glacial melt. The results of field and cold-room measurements indicate that both L. glaciale and Clathromorphum sp. had low calcification and photosynthetic rates during the Greenland summer (2015 and 2016), with maximum of 1.225 ± 0.17 or 0.002 ± 0.023 μmol CaCO3 · g-1 · h-1 and -0.007 ±0.003 or -0.004 ± 0.001 mg O2 · L-1 · h-1 in each species respectively. Mesocosm experiments indicate L. glaciale is a seasonal responder; photosynthetic and calcification rates increase with annual light cycles. Furthermore, metabolic processes in L. glaciale were negatively influenced by low salinity; positive growth rates only occurred in marine treatments where individuals accumulated an average of 1.85 ± 1.73 mg · d-1 of biomass through summer. These results indicate high freshwater input to the Godthåbsfjord region may drive the low abundance of L. glaciale, and could decrease species distribution as climate change increases freshwater input to the Arctic marine system via enhanced ice sheet runoff and glacier calving.Peer reviewedFinal Accepted Versio

Quantum theory of massless (p,0)-forms

We describe the quantum theory of massless (p,0)-forms that satisfy a suitable holomorphic generalization of the free Maxwell equations on Kaehler spaces. These equations arise by first-quantizing a spinning particle with a U(1)-extended local supersymmetry on the worldline. Dirac quantization of the spinning particle produces a physical Hilbert space made up of (p,0)-forms that satisfy holomorphic Maxwell equations coupled to the background Kaehler geometry, containing in particular a charge that measures the amount of coupling to the U(1) part of the U(d) holonomy group of the d-dimensional Kaehler space. The relevant differential operators appearing in these equations are a twisted exterior holomorphic derivative and its hermitian conjugate (twisted Dolbeault operators with charge q). The particle model is used to obtain a worldline representation of the one-loop effective action of the (p,0)-forms. This representation allows to compute the first few heat kernel coefficients contained in the local expansion of the effective action and to derive duality relations between (p,0) and (d-p-2,0)-forms that include a topological mismatch appearing at one-loop.Comment: 32 pages, 3 figure

Membrane Partitioning: “Classical” and “Nonclassical” Hydrophobic Effects

The free energy of transfer of nonpolar solutes from water to lipid bilayers is often dominated by a large negative enthalpy rather than the large positive entropy expected from the hydrophobic effect. This common observation has led to the idea that membrane partitioning is driven by the “nonclassical” hydrophobic effect. We examined this phenomenon by characterizing the partitioning of the well-studied peptide melittin using isothermal titration calorimetry (ITC) and circular dichroism (CD). We studied the temperature dependence of the entropic (−TΔS) and enthalpic (ΔH) components of free energy (ΔG) of partitioning of melittin into lipid membranes made of various mixtures of zwitterionic and anionic lipids. We found significant variations of the entropic and enthalpic components with temperature, lipid composition and vesicle size but only small changes in ΔG (entropy–enthalpy compensation). The heat capacity associated with partitioning had a large negative value of about −0.5 kcal mol−1 K−1. This hallmark of the hydrophobic effect was found to be independent of lipid composition. The measured heat capacity values were used to calculate the hydrophobic-effect free energy ΔGhΦ, which we found to dominate melittin partitioning regardless of lipid composition. In the case of anionic membranes, additional free energy comes from coulombic attraction, which is characterized by a small effective peptide charge due to the lack of additivity of hydrophobic and electrostatic interactions in membrane interfaces [Ladokhin and White J Mol Biol 309:543–552, 2001]. Our results suggest that there is no need for a special effect—the nonclassical hydrophobic effect—to describe partitioning into lipid bilayers

All solutions of the localization equations for N=2 quantum black hole entropy

We find the most general bosonic solution to the localization equations describing the contributions to the quantum entropy of supersymmetric black holes in four-dimensional N=2 supergravity coupled to n_v vector multiplets. This requires the analysis of the BPS equations of the corresponding off-shell supergravity (including fluctuations of the auxiliary fields) with AdS2 \times S2 attractor boundary conditions. Our work completes and extends the results of arXiv:1012.0265 that were obtained for the vector multiplet sector, to include the fluctuations of all the fields of the off-shell supergravity. We find that, when the auxiliary SU(2) gauge field strength vanishes, the most general supersymmetric configuration preserving four supercharges is labelled by n_v+1 real parameters corresponding to the excitations of the conformal mode of the graviton and the scalars of the n_v vector multiplets. In the general case, the localization manifold is labelled by an additional SU(2) triplet of one-forms and a scalar function.Comment: 27 page