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Register a new userRenormalized Effective Actions in Radially Symmetric Backgrounds: Exact Calculations Versus Approximation Methods
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Our previously-developed calculational method (the partial wave cutoff method) is employed to evaluate explicitly scalar one-loop effective actions in a class of radially symmetric background gauge fields. Our method proves to be particularly effective when it is used in conjunction with a systematic WKB series for the large partial wave contribution to the effective action. By comparing these numerically exact calculations against the predictions based on the large mass expansion and derivative expansion, we discuss the validity ranges of the latter approximation methods.
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A class of noncanonical effective potentials is introduced allowing stable, radially symmetric, solutions to first order Bogomolnyi equations for a real scalar field in a fixed spacetime background. This class of effective potentials generalizes those found previously by Bazeia, Menezes, and Menezes [Phys.Rev.Lett. 91 (2003) 241601] for radially symmetric defects in a flat spacetime. Use is made of the on-shell method introduced by Atmaja and Ramadhan [Phys.Rev.D 90 (2014) 10, 105009] of reducing the second order equation of motion to a first order one, along with a constraint equation. This method and class of potentials admits radially symmetric, stable solutions for four dimensional static, radially symmetric spacetimes. Stability against radial fluctuations is established with a modified version of Derricks theorem, along with demonstrating that the radial stress vanishes. Several examples of scalar field configurations are given.
The inferred value of the relic density from cosmological observations has reached a precision that is akin to that of the LEP precision measurements. This level of precision calls for the evaluation of the annihilation cross sections of dark matter that goes beyond tree-level calculations as currently implemented in all codes for the computation of the relic density. In supersymmetry radiative corrections are known to be large and thus must be implemented. Full one-loop radiative corrections for many annihilation processes have been performed. It is important to investigate whether the bulk of these corrections can be parameterised through an improved Born approximation that can be implemented as a selection of form factors to a tree-level code. This paper is a second in a series that addresses this issue. After having provided these form factors for the annihilation of the neutralinos into fermions, which cover the case of a bino-like LSP (Lightest Supersymmetric Particle), we turn our attention here to a higgsino-like dark matter candidate through its annihilation into $ZZ$. We also investigate the cases of a mixed LSP. In all cases we compare the performance of the form factor approach with the result of a full one-loop correction. We also study the issue of the renormalisation scheme dependence. An illustration of the phenomenon of non decoupling of the heavy sfermions that takes place for the annihilation of the lightest neutralino into $ZZ$ is also presented.
We relate the non-perturbative exact results in supersymmetry to perturbation theory using several different methods: instanton calculations at weak or strong coupling, a method using gaugino condensation and another method relating strong and weak coupling. This allows many precise numerical checks of the consistency of these methods, especially the amplitude of instanton effects, and of the network of exact solutions in supersymmetry. However, there remain difficulties with the instanton computations at strong coupling.
We use the evolution operator method to find the one-loop effective action of scalar and spinor QED in electric field backgrounds in terms of the Bogoliubov coefficient between the ingoing and the outgoing vacua. We obtain the exact one-loop effective action for a Sauter-type electric field, E_0 sech^2 (t/tau), and show that the imaginary part correctly yields the vacuum persistence. The renormalized effective action shows the general relation between the vacuum persistence and the total mean number of created pairs for the constant and the Sauter-type electric field.
We argue that an effective field theory of local fluid elements captures the constraints on hydrodynamic transport stemming from the presence of quantum anomalies in the underlying microscopic theory. Focussing on global current anomalies for an arbitrary flavour group, we derive the anomalous constitutive relations in arbitrary even dimensions. We demonstrate that our results agree with the constraints on anomaly governed transport derived hitherto using a local version of the second law of thermodynamics. The construction crucially uses the anomaly inflow mechanism and involves a novel thermofield double construction. In particular, we show that the anomalous Ward identities necessitate non-trivial interaction between the two parts of the Schwinger-Keldysh contour.
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