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

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

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

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

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

Quantum theories of (p,q)-forms

We describe quantum theories for massless (p,q)-forms living on Kaehler spaces. In particular we consider four different types of quantum theories: two types involve gauge symmetries and two types are simpler theories without gauge invariances. The latter can be seen as building blocks of the former. Their equations of motion can be obtained in a natural way by first-quantizing a spinning particle with a U(2)-extended supersymmetry on the worldline. The particle system contains four supersymmetric charges, represented quantum mechanically by the Dolbeault operators and their hermitian conjugates. After studying how the (p,q)-form field theories emerge from the particle system, we investigate their one loop effective actions, identify corresponding heat kernel coefficients, and derive exact duality relations. The dualities are seen to include mismatches related to topological indices and analytic torsions, which are computed as Tr(-1)^F and Tr[(-1)^F F] in the first quantized supersymmetric nonlinear sigma model for a suitable fermion number operator F.Comment: 44 pages, 2 figures, a reference adde

On duality symmetry in perturbative quantum theory

Non-compact symmetries of extended 4d supergravities involve duality rotations of vectors and thus are not manifest off-shell invariances in standard "second-order" formulation. To study how such symmetries are realised in the quantum theory we consider examples in 2 dimensions where vector-vector duality is replaced by scalar-scalar one. Using a "doubled" formulation, where fields and their momenta are treated on an equal footing and the duality becomes a manifest symmetry of the action (at the expense of Lorentz symmetry), we argue that the corresponding on-shell quantum effective action or S-matrix are duality symmetric as well as Lorentz invariant. The simplest case of discrete Z_2 duality corresponds to a symmetry of the S-matrix under flipping the sign of the negative-chirality scalars in 2 dimensions or phase rotations of chiral (definite-helicity) parts of vectors in 4 dimensions. We also briefly discuss some 4d models and comment on implications of our analysis for extended supergravities.Comment: 21 pages, Latex v2: comments and references added v3: references and minor comments adde

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

Boundary Conditions and Unitarity: the Maxwell-Chern-Simons System in AdS_3/CFT_2

We consider the holography of the Abelian Maxwell-Chern-Simons (MCS) system in Lorentzian three-dimensional asymptotically-AdS spacetimes, and discuss a broad class of boundary conditions consistent with conservation of the symplectic structure. As is well-known, the MCS theory contains a massive sector dual to a vector operator in the boundary theory, and a topological sector consisting of flat connections dual to U(1) chiral currents; the boundary conditions we examine include double-trace deformations in these two sectors, as well as a class of boundary conditions that mix the vector operators with the chiral currents. We carefully study the symplectic product of bulk modes and show that almost all such boundary conditions induce instabilities and/or ghost excitations, consistent with violations of unitarity bounds in the dual theory.Comment: 50+1 pages, 6 figures, PDFLaTeX; v2: added references, corrected typo

On the perturbative S-matrix of generalized sine-Gordon models

Motivated by its relation to the Pohlmeyer reduction of AdS_5 x S^5 superstring theory we continue the investigation of the generalized sine-Gordon model defined by SO(N+1)/SO(N) gauged WZW theory with an integrable potential. Extending our previous work (arXiv:0912.2958) we compute the one-loop two-particle S-matrix for the elementary massive excitations. In the N = 2 case corresponding to the complex sine-Gordon theory it agrees with the charge-one sector of the quantum soliton S-matrix proposed in hep-th/9410140. In the case of N > 2 when the gauge group SO(N) is non-abelian we find a curious anomaly in the Yang-Baxter equation which we interpret as a gauge artifact related to the fact that the scattered particles are not singlets under the residual global subgroup of the gauge group