Conservation of the stress tensor in perturbative interacting quantum field theory in curved spacetimes

We propose additional conditions (beyond those considered in our previous papers) that should be imposed on Wick products and time-ordered products of a free quantum scalar field in curved spacetime. These conditions arise from a simple ``Principle of Perturbative Agreement'': For interaction Lagrangians $L_1$ that are such that the interacting field theory can be constructed exactly--as occurs when $L_1$ is a ``pure divergence'' or when $L_1$ is at most quadratic in the field and contains no more than two derivatives--then time-ordered products must be defined so that the perturbative solution for interacting fields obtained from the Bogoliubov formula agrees with the exact solution. The conditions derived from this principle include a version of the Leibniz rule (or ``action Ward identity'') and a condition on time-ordered products that contain a factor of the free field $\phi$ or the free stress-energy tensor $T_{ab}$. The main results of our paper are (1) a proof that in spacetime dimensions greater than 2, our new conditions can be consistently imposed in addition to our previously considered conditions and (2) a proof that, if they are imposed, then for {\em any} polynomial interaction Lagrangian $L_1$ (with no restriction on the number of derivatives appearing in $L_1$), the stress-energy tensor $\Theta_{ab}$ of the interacting theory will be conserved. Our work thereby establishes (in the context of perturbation theory) the conservation of stress-energy for an arbitrary interacting scalar field in curved spacetimes of dimension greater than 2. Our approach requires us to view time-ordered products as maps taking classical field expressions into the quantum field algebra rather than as maps taking Wick polynomials of the quantum field into the quantum field algebra.Comment: 88 pages, latex, no figures, v2: changes in the proof of proposition 3.

Perturbative Construction of Models of Algebraic Quantum Field Theory

We review the construction of models of algebraic quantum field theory by renormalized perturbation theory.Comment: 38 page

Supersymmetric Field-Theoretic Models on a Supermanifold

We propose the extension of some structural aspects that have successfully been applied in the development of the theory of quantum fields propagating on a general spacetime manifold so as to include superfield models on a supermanifold. We only deal with the limited class of supermanifolds which admit the existence of a smooth body manifold structure. Our considerations are based on the Catenacci-Reina-Teofillatto-Bryant approach to supermanifolds. In particular, we show that the class of supermanifolds constructed by Bonora-Pasti-Tonin satisfies the criterions which guarantee that a supermanifold admits a Hausdorff body manifold. This construction is the closest to the physicist's intuitive view of superspace as a manifold with some anticommuting coordinates, where the odd sector is topologically trivial. The paper also contains a new construction of superdistributions and useful results on the wavefront set of such objects. Moreover, a generalization of the spectral condition is formulated using the notion of the wavefront set of superdistributions, which is equivalent to the requirement that all of the component fields satisfy, on the body manifold, a microlocal spectral condition proposed by Brunetti-Fredenhagen-K\"ohler.Comment: Final version to appear in J.Math.Phy

Batalin-Vilkovisky formalism in perturbative algebraic quantum field theory

On the basis of a thorough discussion of the Batalin-Vilkovisky formalism for classical field theory presented in our previous publication, we construct in this paper the Batalin-Vilkovisky complex in perturbatively renormalized quantum field theory. The crucial technical ingredient is a proof that the renormalized time-ordered product is equivalent to the pointwise product of classical field theory. The renormalized Batalin-Vilkovisky algebra is then the classical algebra but written in terms of the time-ordered product, together with an operator which replaces the ill defined graded Laplacian of the unrenormalized theory. We identify it with the anomaly term of the anomalous Master Ward Identity of Brennecke and D\"utsch. Contrary to other approaches we do not refer to the path integral formalism and do not need to use regularizations in intermediate steps.Comment: 34 page

Further restrictions on the topology of stationary black holes in five dimensions

We place further restriction on the possible topology of stationary asymptotically flat vacuum black holes in 5 spacetime dimensions. We prove that the horizon manifold can be either a connected sum of Lens spaces and "handles" $S^1 \times S^2$, or the quotient of $S^3$ by certain finite groups of isometries (with no "handles"). The resulting horizon topologies include Prism manifolds and quotients of the Poincare homology sphere. We also show that the topology of the domain of outer communication is a cartesian product of the time direction with a finite connected sum of $\mathbb R^4,S^2 \times S^2$'s and $CP^2$'s, minus the black hole itself. We do not assume the existence of any Killing vector beside the asymptotically timelike one required by definition for stationarity.Comment: LaTex, 22 pages, 9 figure

Post-test simulations for the NACIE-UP benchmark by STH codes

This paper illustrates the results obtained in the last phase of the NACIE-UP benchmark activity foreseen inside the EU SESAME Project. The purpose of this research activity, performed by system thermal–hydraulic (STH) codes, is finalized to the improvement, development and validation of existing STH codes for Heavy Liquid Metal (HLM) systems. All the participants improved their modelling of the NACIE-UP facility, respect to the initial blind simulation phase, adopting the actual experimental boundary conditions and reducing as much as possible sources of uncertainty in their numerical model. Four different STH codes were employed by the participants to the benchmark to model the NACIE-UP facility, namely: CATHARE for ENEA, ATHLET for GRS, RELAP5-3D© for the “Sapienza” University of Rome and RELAP5/Mod3.3(modified) for the University of Pisa. Three reference tests foreseen in the NACIE-UP benchmark and carried out at ENEA Brasimone Research Centre were analysed from four participants. The data from the post-test analyses, performed independently by the participant using different STH codes, were compared together and with the available experimental results and critically discussed

Towards a 4d/2d correspondence for Sicilian quivers

We study the 4d/2d AGT correspondence between four-dimensional instanton counting and two-dimensional conformal blocks for generalized SU(2) quiver gauge theories coming from punctured Gaiotto curves of arbitrary genus. We propose a conformal block description that corresponds to the elementary SU(2) trifundamental half-hypermultiplet, and check it against Sp(1)-SO(4) instanton counting.Comment: 39 pages, 11 figure

A Comparison of Turning Kinematics at Different Amplitudes during Standing Turns between Older and Younger Adults

It is well-established that processes involving changing direction or turning in which either or both standing and walking turns are utilized involve coordination of the whole-body and stepping characteristics. However, the turn context and whole-body coordination have not been fully explored during different turning amplitudes. For these reasons, this present study aimed to determine the effects of turning amplitude on whole-body coordination. The findings from this study can be utilized to inform the rationale behind fall prevention factors and to help design an exercise strategy to address issues related to amplitude of turning in older adults. Twenty healthy older and twenty healthy younger adults were asked to complete standing turns on level ground using three randomly selected amplitudes, 90°, 135° and 180°, at their self-selected turn speed. Turning kinematics and stepping variables were recorded using Inertial Measurement Units. Analysis of the data was carried out using Mixed Model Analysis of Variance with two factors (2 groups × 3 turning amplitudes) and further post hoc pairwise analysis to examine differences between factors. There were significant interaction effects (p < 0.05) between the groups and turning amplitudes for step duration and turn speed. Further analysis using Repeated Measure Analysis of Variance tests determined a main effect of amplitude on step duration and turn speed within each group. Furthermore, post hoc pairwise comparisons revealed that the step duration and turn speed increased significantly (p < 0.001) with all increases in turning amplitude in both groups. In addition, significant main effects for group and amplitudes were seen for onset latency of movement for the head, thorax, pelvis, and feet, and for peak head–thorax and peak head–pelvis angular separations and stepping characteristics, which all increased with turn amplitude and showed differences between groups. These results suggest that large amplitude turns result in a change in turning and stepping kinematics. Therefore, when assessing the turning characteristics of older adults or those in frail populations, the turning amplitude should be taken into account during turning, and could be gradually increased to challenge motor control as part of exercise falls prevention strategies

The gravity duals of SO/USp superconformal quivers

We study the gravity duals of SO/USp superconformal quiver gauge theories realized by M5-branes wrapping on a Riemann surface ("G-curve") together with a Z_2-quotient. When the G-curve has no punctures, the gravity solutions are classified by the genus g of the G-curve and the torsion part of the four-form flux G_4. We also find that there is an interesting relation between anomaly contributions from two mysterious theories: T_{SO(2N)} theory with SO(2N)^3 flavor symmetry and \tilde{T}_{SO(2N)} theory with SO(2N) x USp(2N-2)^2 flavor symmetry. The dual gravity solutions for various SO/USp-type tails are also studied.Comment: 27 pages, 13 figures; v2 minor corrections, typos corrected, Figure 13 replaced, references adde

Asymptotic generators of fermionic charges and boundary conditions preserving supersymmetry

We use a covariant phase space formalism to give a general prescription for defining Hamiltonian generators of bosonic and fermionic symmetries in diffeomorphism invariant theories, such as supergravities. A simple and general criterion is derived for a choice of boundary condition to lead to conserved generators of the symmetries on the phase space. In particular, this provides a criterion for the preservation of supersymmetries. For bosonic symmetries corresponding to diffeomorphisms, our prescription coincides with the method of Wald et al. We then illustrate these methods in the case of certain supergravity theories in $d=4$. In minimal AdS supergravity, the boundary conditions such that the supercharges exist as Hamiltonian generators of supersymmetry transformations are unique within the usual framework in which the boundary metric is fixed. In extended ${\mathcal N}=4$ AdS supergravity, or more generally in the presence of chiral matter superfields, we find that there exist many boundary conditions preserving ${\mathcal N}=1$ supersymmetry for which corresponding generators exist. These choices are shown to correspond to a choice of certain arbitrary boundary ``superpotentials,'' for suitably defined ``boundary superfields.'' We also derive corresponding formulae for the conserved bosonic charges, such as energy, in those theories, and we argue that energy is always positive, for any supersymmetry-preserving boundary conditions. We finally comment on the relevance and interpretation of our results within the AdS-CFT correspondence.Comment: 45 pages, Latex, no figures, v2: extended discussion of positive energy theorem and explicit form of fermionic generators, references adde