Discrete and continuous symmetries in multi-Higgs-doublet models

We consider the Higgs sector of multi-Higgs-doublet models in the presence of simple symmetries relating the various fields. We construct basis invariant observables which may in principle be used to detect these symmetries for any number of doublets. A categorization of the symmetries into classes is required, which we perform in detail for the case of two and three Higgs doublets.Comment: 13 pages, RevTex, references adde

On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 3: Mass inflation and extendibility of the solutions

This paper is the third part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system with a cosmological constant $\Lambda$, with the data on the outgoing initial null hypersurface given by a subextremal Reissner-Nordstrom black hole event horizon, study the future extendibility of the corresponding maximal globally hyperbolic development as a "suitably regular" Lorentzian manifold. In the first part of this series we established the well posedness of the characteristic problem, whereas in the second part we studied the stability of the radius function at the Cauchy horizon. In this third and final paper we show that, depending on the decay rate of the initial data, mass inflation may or may not occur. When the mass is controlled, it is possible to obtain continuous extensions of the metric across the Cauchy horizon with square integrable Christoffel symbols. Under slightly stronger conditions, we can bound the gradient of the scalar field. This allows the construction of (non-isometric) extensions of the maximal development which are classical solutions of the Einstein equations. Our results provide evidence against the validity of the strong cosmic censorship conjecture when $\Lambda>0$.Comment: 48 pages, 5 figures; v2: some presentation changes, mostly in the Introduction; v3: substantial changes in Section 5; v4: expanded Introduction; some presentation changes; matches final published versio

On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 2: Structure of the solutions and stability of the Cauchy horizon

This paper is the second part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system with a cosmological constant $\Lambda$, with the data on the outgoing initial null hypersurface given by a subextremal Reissner-Nordstrom black hole event horizon, study the future extendibility of the corresponding maximal globally hyperbolic development as a "suitably regular" Lorentzian manifold. In the first paper of this sequence, we established well posedness of the characteristic problem with general initial data. In this second paper, we generalize the results of Dafermos on the stability of the radius function at the Cauchy horizon by including a cosmological constant. This requires a considerable deviation from the strategy followed by Dafermos, focusing on the level sets of the radius function instead of the red-shift and blue-shift regions. We also present new results on the global structure of the solution when the free data is not identically zero in a neighborhood of the origin. In the third and final paper, we will consider the issue of mass inflation and extendibility of solutions beyond the Cauchy horizon.Comment: 44 pages, 13 figures; v2: a few small changes; v3: a paragraph was added in the Introduction, minor clarifications were made thoughout, the list of references was expanded, matches final published versio

Measuring the importance of the uniform nonsynchronization hypothesis

In this paper we critically reappraise some measures of the importance of time-dependent price setting rules and propose an alternative way to gauge the significance of this type of price setting behaviour. The merits of the proposed measure are highlighted in an application using micro-data. Our results suggest that a large proportion of price trajectories may be compatible with simple time-dependent price setting mechanisms but the strength of this evidence very much depends on the way that is used to evaluate the importance of this type of behaviour. JEL Classification: D40, E31, L11perfect synchronization, Time-dependent price setting models, uniform staggering

Time or state dependent price setting rules? Evidence from Portuguese micro data

In this paper we analyse the ability of time and state dependent price setting rules to explain durations of price spells or the probability of changing prices. Our results suggest that simple time dependent models cannot be seen as providing a reasonable approximation to the data and that state dependent models are required to fully characterise the price setting behaviour of Portuguese firms. Inflation, the level of economic activity and the magnitude of the last price change emerge as relevant variables affecting the probability of changing prices. Moreover, it is seen that the impact differs for negative and positive values of these covariates. JEL Classification: C41, D40, E31CPI data, Hazard functions, inflation

Basis invariant conditions for supersymmetry in the two-Higgs-doublet model

The minimal supersymmetric standard model involves a rather restrictive Higgs potential with two Higgs fields. Recently, the full set of classes of symmetries allowed in the most general two Higgs doublet model was identified; these classes do not include the supersymmetric limit as a particular class. Thus, a physically meaningful definition of the supersymmetric limit must involve the interaction of the Higgs sector with other sectors of the theory. Here we show how one can construct basis invariant probes of supersymmetry involving both the Higgs sector and the gaugino-higgsino Higgs interactions.Comment: RevTex, 11 pages, v2-small section adde