1,720,982 research outputs found
The generalized hypergeometric structure of the ward identities of CFT's in momentum Space in d > 2
Full text linkWe review the emergence of hypergeometric structures (of F4 Appell functions) from the conformalWard identities (CWIs) in conformal field theories (CFTs) in dimensions d > 2. We illustrate the case of scalar 3-and 4-point functions. 3-point functions are associated to hypergeometric systems with four independent solutions. For symmetric correlators, they can be expressed in terms of a single 3K integral-functions of quadratic ratios of momenta-which is a parametric integral of three modified Bessel K functions. In the case of scalar 4-point functions, by requiring the correlator to be conformal invariant in coordinate space as well as in some dual variables (i.e., dual conformal invariant), its explicit expression is also given by a 3K integral, or as a linear combination of Appell functions which are now quartic ratios of momenta. Similar expressions have been obtained in the past in the computation of an infinite class of planar ladder (Feynman) diagrams in perturbation theory, which, however, do not share the same (dual conformal/conformal) symmetry of our solutions. We then discuss some hypergeometric functions of 3 variables, which define 8 particular solutions of the CWIs and correspond to Lauricella functions. They can also be combined in terms of 4K integral and appear in an asymptotic description of the scalar 4-point function, in special kinematical limits
The general 3-graviton vertex (TTT) of conformal field theories in momentum space in d = 4
Full text linkWe present a study of the correlation function of three stress-energy tensors in d dimensions using free field theory realizations, and compare them to the exact solutions of their conformal Ward identities (CWI's) obtained by a general approach in momentum space. The identification of the corresponding form factors is performed within a reconstruction method, based on the identification of the transverse traceless components (Ai) of the same correlator. The solutions of the primary CWI' s are found by exploiting the universality of the Fuchsian indices of the conformal operators and a re-arrangement of the corresponding inhomogenous hypergeometric systems. We confirm the number of constants in the solution of the primary CWI's of previous analysis. In our comparison with perturbation theory, we discuss scalar, fermion and spin 1 exchanges at 1-loop in dimensional regularization. Explicit checks in d=3,4,5 prove the consistency of this correspondence. By matching the 3 constants of the CFT solution with the 3 free field theory sectors available in d=4, the general solutions of the conformal constraints is expressed just in terms of ordinary scalar 2- and 3-point functions (B0,C0). We show how the renormalized d=4 TTT vertex separates naturally into the sum of a traceless and an anomaly part, the latter determined by the anomaly functional and generated by the renormalization of the correlator in dimensional regularization. The result confirms the emergence of anomaly poles and effective massless exchanges as a specific signature of conformal anomalies in momentum space, directly connected to the renormalization of the corresponding gravitational vertices, generalizing the behaviour found for the TJJ vertex in previous works
Contactless energy transfer in adverse environment using rectennas
No full textThe application of a wireless energy transfer system to a rotating shaft is analyzed in this paper
Nonlocal Gravity, Dark Energy and Conformal Symmetry: Testing the Hierarchies of Anomaly-Induced Actions
Full text linkConformal back-reaction generates cosmological models where the trace anomaly reflects the breaking of Weyl invariance. Analyzing these actions yields a dynamic approach to dark energy through anomaly-induced actions (AIAs), that are variational solutions of the trace anomaly functional constraint. Expanded around Minkowski space, they produce semiclassical correlators subject to hierarchical anomalous Ward identities, tied to conformal symmetry and diffeomorphism invariance. We focus on comparing the hierarchy of a specific 4-point function, particularly the 2-gravitons-2-photons correlator (TTJJ) , generated by AIAs, to free field theory realizations of the same correlator. We observe that the free field theory original hierarchy splits into one ordinary and one anomalous hierarchy, both satisfying the conservation Ward identities from diffeomorphism invariance. However, we find that the anomalous hierarchy derived from ordinary AIAs in both the Riegert or Fradkin-Vilkovisky gauges, are either affected by double poles or violate the hierarchy of the trace Ward identity, respectively. We show that correct forms of the anomalous hierarchies of 4-point functions (for the TTTT and TTJJ), identified in a perturbative free field theory expansion around flat space, are characterised by anomaly poles, corresponding to a curvature expansion in R□−1 , together with Weyl invariant terms. We derive the effective action that generates the correct form of the hierarchy for the TTJJ
A coil model for voltage distribution and electrical insulation analysis
No full textThe voltage distribution inside a machine's winding is analyzed in this paper. The use of a simple distributed parameters coil model allows to predict, in a qualitative way, the value of the peak voltage as a function of the winding length. Thanks to a simple algorithm, the voltage peak distribution is analyzed as a function of the coil constructive parameters like the capacitance-to- ground and the inter-turn capacitance. Remarks on the effects of the insulation thickness variation for the winding are made. Simulation results and Finite Element Method (FEM) analysis are presented for different cases
CFT correlators and CP-violating trace anomalies
Full text linkAbstract We analyze the parity-odd correlators ⟨ J J O ⟩ odd , ⟨ J J T ⟩ odd , ⟨ T T O ⟩ odd and ⟨ T T T ⟩ odd in momentum space, constrained by conformal Ward identities, extending our former investigation of the parity-odd chiral anomaly vertex. We investigate how the presence of parity-odd trace anomalies affect such correlators. Motivations for this study come from holography, early universe cosmology and from a recent debate on the chiral trace anomaly of a Weyl fermion. In the current CFT analysis, O can be either a scalar or a pseudoscalar operator and it can be identified with the trace of the stress–energy tensor. We find that the ⟨ J J O ⟩ odd and ⟨ T T O ⟩ odd can be different from zero in a CFT. This occurs when the conformal dimension of the scalar operator is Δ 3 = 4 , as in the case of O = T μ μ . Moreover, if we assume the existence of parity-odd trace anomalies, the conformal ⟨ J J T ⟩ odd and ⟨ T T T ⟩ odd are nonzero. In particular, in the case of ⟨ J J T ⟩ odd the transverse–traceless component is constrained to vanish, and the correlator is determined only by the trace part with the anomaly pole
Three-wave and four-wave interactions in the 4d Einstein Gauss-Bonnet (EGB) and Lovelock theories
Full text linkWe derive the conformal constraints satisfied by classical vertices of a (Einstein) Gauss-Bonnet theory around flat space, in general dimensions and at d=4 (4d EGB). In 4d EGB they are obtained by a singular limit of the integral of the Euler-Poincarè density. Our analysis exploits the relation between this theory and the conformal anomaly action, which allows to uncover some interesting features of the GB vertex at cubic and quartic level. If we introduce a conformal decomposition of the metric, the resulting theory can be formulated in two different versions, which are regularization dependent, a local one which is quartic in the dilaton field, and a nonlocal one, with a quadratic dilaton. The nonlocal version is derived by a finite redefinition of the GB density with the inclusion of a (d−4)R2 correction, before performing the singular d→4 limit. In the local version of the theory, we show how the independent dynamics of the metric and of the dilaton are interwinded by a classical trace identity. Three-gravitational wave interactions can be organised in a nontrivial way by using directly the nonlocal 4d EGB version of the theory. This is possible thanks to the consistency of such formulation - only up to 3-point functions - directly inherited from the conformal anomaly (Riegert) action. The constraints satisfied by the vertices are classical, hierarchical Ward identities. At quartic level, similar relations are derived, borrowing from the analysis of the counterterms of the 4T correlators of the conformal anomaly action, as defined by a perturbative expansion. For d≠4 these constraints hold also for Lovelock actions. They can be extended to higher order topological invariants in such class of theories
A model of magnetostrictive actuators for active vibration control
No full textOne of the most frequent application of magnetostrictive actuator technology is the active structural vibration control (AVC). Magnetostrictive actuators (MA) can deliver high-output forces and relatively high displacements (compared to other emerging actuator technologies) and can be driven at high frequencies: these characteristics make them suitable for a variety of vibration control applications. The use of this technology, however, requires an accurate knowledge of the dynamics of such actuators. The paper introduces a linear model of magnetostrictive actuators hold in a range of frequencies below 2 kHz useful in real time application as AVC. The hypotesis supporting the linearity of the systems are discussed and the theoretical model is presented. Finally the model is validated by testing two different models of magnetostrictive actuators and comparing experimental results with the theoretical ones
4D Einstein Gauss-Bonnet Gravity without a Dilaton
Full text linkA nonlocal version of Einstein-Gauss Bonnet (EGB) gravity can be generated by a procedure that follows closely the steps of the derivation of the conformal anomaly effective action. The action is obtained using a Weyl decomposition of the metric, with the conformal factor removed by a finite renormalization of the topological term. We outline the mains steps in the derivation of this action, stressing on the analogies and differences respect to the anomaly action and to the ordinary 4d EGB theory formulated as a special version of dilaton gravity. These formulations allow a systematic investigation of the nonlocal R−1 corrections to General Relativity. In the case of conformal anomaly action they are motivated by the generation of a conformal backreaction, due to the breaking of conformal symmetry in the early universe
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