Homotopy transfer and effective field theory I: tree-level

We use the dictionary between general field theories and strongly homotopyalgebras to provide an algebraic formulation of the procedure of integratingout of degrees of freedom in terms of homotopy transfer. This includes moregeneral effective theories in which some massive modes are kept while othermodes of a comparable mass scale are integrated out, as first explored by Senin the context of closed string field theory. We treatL∞-algebras both in termsof a nilpotent coderivation and, on the dual space, in terms of a nilpotentderivation (corresponding to the BRST charge of the field theory) and provideexplicit formulas for homotopy transfer. These are then shown to govern theintegrating out of degrees of freedom at tree level, while the generalization toloop level will be explored in a sequel to this paper

Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds

We develop quantization techniques for describing the nonassociative geometry probed by closed strings in flat non-geometric R-flux backgrounds M. Starting from a suitable Courant sigma-model on an open membrane with target space M, regarded as a topological sector of closed string dynamics in R-space, we derive a twisted Poisson sigma-model on the boundary of the membrane whose target space is the cotangent bundle T^*M and whose quasi-Poisson structure coincides with those previously proposed. We argue that from the membrane perspective the path integral over multivalued closed string fields in Q-space is equivalent to integrating over open strings in R-space. The corresponding boundary correlation functions reproduce Kontsevich's deformation quantization formula for the twisted Poisson manifolds. For constant R-flux, we derive closed formulas for the corresponding nonassociative star product and its associator, and compare them with previous proposals for a 3-product of fields on R-space. We develop various versions of the Seiberg-Witten map which relate our nonassociative star products to associative ones and add fluctuations to the R-flux background. We show that the Kontsevich formula coincides with the star product obtained by quantizing the dual of a Lie 2-algebra via convolution in an integrating Lie 2-group associated to the T-dual doubled geometry, and hence clarify the relation to the twisted convolution products for topological nonassociative torus bundles. We further demonstrate how our approach leads to a consistent quantization of Nambu-Poisson 3-brackets.Comment: 52 pages; v2: references adde

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

On "New Massive" 4D Gravity

We construct a four-dimensional (4D) gauge theory that propagates, unitarily, the five polarization modes of a massive spin-2 particle. These modes are described by a "dual" graviton gauge potential and the Lagrangian is 4th-order in derivatives. As the construction mimics that of 3D "new massive gravity", we call this 4D model (linearized) "new massive dual gravity". We analyse its massless limit, and discuss similarities to the Eddington-Schroedinger model.Comment: 17 pages, v2 : version published in JHE

Parent formulation at the Lagrangian level

The recently proposed first-order parent formalism at the level of equations of motion is specialized to the case of Lagrangian systems. It is shown that for diffeomorphism-invariant theories the parent formulation takes the form of an AKSZ-type sigma model. The proposed formulation can be also seen as a Lagrangian version of the BV-BRST extension of the Vasiliev unfolded approach. We also discuss its possible interpretation as a multidimensional generalization of the Hamiltonian BFV--BRST formalism. The general construction is illustrated by examples of (parametrized) mechanics, relativistic particle, Yang--Mills theory, and gravity.Comment: 26 pages, discussion of the truncation extended, typos corrected, references adde

Abnormal function of the vasopressin-cyclic-AMP-aquaporin2 axis during urine concentrating and diluting in patients with reduced renal function. A case control study

<p>Abstract</p> <p>Background</p> <p>The kidneys ability to concentrate and dilute urine is deteriorated during progressive renal insufficiency. We wanted to test the hypothesis that these phenomena could be attributed to an abnormal function of the principal cells in the distal part of the nephron.</p> <p>Methods</p> <p>Healthy control subjects and patients with chronic kidney diseases were studied. Group 1 comprised healthy subjects, n = 10. Groups 2-4 comprised patients with chronic kidney disease (Group 2, n = 14, e-GFR ? 90 m1/min; Group 3, n = 11, 60 m1/min ? e-GFR < 90 ml/min; and Group 4, n = 16, 15 ml/min ? e-GFR < 60 ml/min). The subjects collected urine during 24 hours. A urine concentrating test was done by thirsting during the following 12 hours. Thereafter, a urine diluting test was performed with a water load of 20 ml/kg body weight. The effect variables were urinary excretions of aquaporin2 (u-AQP2), cyclic-AMP (u-c-AMP), urine volume (UV), free water clearance (C_H2O), urine osmolarity (u-Osm), and plasma arginine vasopressin (p-AVP).</p> <p>Results</p> <p>After fluid deprivation, u-Osm increased. In all groups, UV and C_H2Odecreased and u-AQP2 and u-c-AMP increased in Groups 1 and 2, but were unchanged in Group 3 and 4. P-AVP was significantly higher in Group 4 than in the other groups. During urine diluting, UV and C_H2Oreached significantly higher levels in Groups 1-3 than Group 4. Both before and after water loading, u-AQP2 and p-AVP were significantly higher and u-c-AMP was significantly lower in Group 4 than the other groups. Estimated-GFR was correlated negatively to p-AVP and positively to u-c-AMP.</p> <p>Conclusions</p> <p>Patients with moderately severe chronic kidney disease have a reduced renal concentrating and diluting capacity compared to both patients with milder chronic kidney disease and healthy control subjects. These phenomena can be attributed, at least partly, to an abnormally decreased response in the AVP-c-AMP-AQP2 axis.</p> <p>ClinicalTrials.Gov Identifier: NCT00313430</p

First order parent formulation for generic gauge field theories

We show how a generic gauge field theory described by a BRST differential can systematically be reformulated as a first order parent system whose spacetime part is determined by the de Rham differential. In the spirit of Vasiliev's unfolded approach, this is done by extending the original space of fields so as to include their derivatives as new independent fields together with associated form fields. Through the inclusion of the antifield dependent part of the BRST differential, the parent formulation can be used both for on and off-shell formulations. For diffeomorphism invariant models, the parent formulation can be reformulated as an AKSZ-type sigma model. Several examples, such as the relativistic particle, parametrized theories, Yang-Mills theory, general relativity and the two dimensional sigma model are worked out in details.Comment: 36 pages, additional sections and minor correction

N = 2 supersymmetric sigma-models and duality

For two families of four-dimensional off-shell N = 2 supersymmetric nonlinear sigma-models constructed originally in projective superspace, we develop their formulation in terms of N = 1 chiral superfields. Specifically, these theories are: (i) sigma-models on cotangent bundles T*M of arbitrary real analytic Kaehler manifolds M; (ii) general superconformal sigma-models described by weight-one polar supermultiplets. Using superspace techniques, we obtain a universal expression for the holomorphic symplectic two-form \omega^{(2,0)} which determines the second supersymmetry transformation and is associated with the two complex structures of the hyperkaehler space T*M that are complimentary to the one induced from M. This two-form is shown to coincide with the canonical holomorphic symplectic structure. In the case (ii), we demonstrate that \omega^{(2,0)} and the homothetic conformal Killing vector determine the explicit form of the superconformal transformations. At the heart of our construction is the duality (generalized Legendre transform) between off-shell N = 2 supersymmetric nonlinear sigma-models and their on-shell N = 1 chiral realizations. We finally present the most general N = 2 superconformal nonlinear sigma-model formulated in terms of N = 1 chiral superfields. The approach developed can naturally be generalized in order to describe 5D and 6D superconformal nonlinear sigma-models in 4D N = 1 superspace.Comment: 31 pages, no figures; V2: reference and comments added, typos corrected; V3: more typos corrected, published versio

Off-Diagonal Deformations of Kerr Metrics and Black Ellipsoids in Heterotic Supergravity

Geometric methods for constructing exact solutions of motion equations with first order $\alpha ^{\prime}$ corrections to the heterotic supergravity action implying a non-trivial Yang-Mills sector and six dimensional, 6-d, almost-K\"ahler internal spaces are studied. In 10-d spacetimes, general parametrizations for generic off-diagonal metrics, nonlinear and linear connections and matter sources, when the equations of motion decouple in very general forms are considered. This allows us to construct a variety of exact solutions when the coefficients of fundamental geometric/physical objects depend on all higher dimensional spacetime coordinates via corresponding classes of generating and integration functions, generalized effective sources and integration constants. Such generalized solutions are determined by generic off-diagonal metrics and nonlinear and/or linear connections. In particular, as configurations which are warped/compactified to lower dimensions and for Levi-Civita connections. The corresponding metrics can have (non) Killing and/or Lie algebra symmetries and/or describe (1+2)-d and/or (1+3)-d domain wall configurations, with possible warping nearly almost-K\"ahler manifolds, with gravitational and gauge instantons for nonlinear vacuum configurations and effective polarizations of cosmological and interaction constants encoding string gravity effects. A series of examples of exact solutions describing generic off-diagonal supergravity modifications to black hole/ ellipsoid and solitonic configurations are provided and analyzed. We prove that it is possible to reproduce the Kerr and other type black solutions in general relativity (with certain types of string corrections) in 4-d and to generalize the solutions to non-vacuum configurations in (super) gravity/ string theories.Comment: latex2e, 44 pages with table of content, v2 accepted to EJPC with minor typos modifications requested by editor and referee and up-dated reference

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