Lorentz violation in the linearized gravity

We study some consequences of the introduction of a Lorentz-violating modification term in the linearized gravity, which leads to modified dispersion relations for gravitational waves in the vacuum. We also discuss possible mechanisms for the induction of such a term in the Lagrangian.Comment: Presented at the Fifth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 28-July 2, 201

CP(N−1)CP^{(N-1)} model in aether-superspace

In this paper we study the dynamical generation of mass in the Lorentz-violating $CP^{(N-1)}$ model defined in two and three-dimensional aether-superspace. We show that even though the model presents a phase structure similar to the usual, Lorentz invariant case, the dynamically generated mass by quantum corrections has a dependence on the Lorentz violating background properties, except for spacelike LV vector parameter. This is to be contrasted with the behavior of the quantum electrodynamics in the two-dimensional aether-superspace, where the dynamical generation of mass was shown to exhibit an explicit dependence on the aether parameters in every possible case.Comment: 18 pages, 4 figure

Matrix Models, Argyres-Douglas singularities and double scaling limits

We construct an N=1 theory with gauge group U(nN) and degree n+1 tree level superpotential whose matrix model spectral curve develops an A_{n+1} Argyres-Douglas singularity. We evaluate the coupling constants of the low-energy U(1)^n theory and show that the large N expansion is singular at the Argyres-Douglas points. Nevertheless, it is possible to define appropriate double scaling limits which are conjectured to yield four dimensional non-critical string theories as proposed by Ferrari. In the Argyres-Douglas limit the n-cut spectral curve degenerates into a solution with n/2 cuts for even n and (n+1)/2 cuts for odd n.Comment: 31 pages, 1 figure; the expression of the superpotential has been corrected and the calculation of the coupling constants of the low-energy theory has been adde

Renormalization Group and Conformal Symmetry Breaking in the Chern-Simons Theory Coupled to Matter

The three-dimensional Abelian Chern-Simons theory coupled to a scalar and a fermionic field of arbitrary charge is considered in order to study conformal symmetry breakdown and the effective potential stability. We present an improved effective potential computation based on two-loop calculations and the renormalization group equation: the later allows us to sum up series of terms in the effective potential where the power of the logarithms are one, two and three units smaller than the total power of coupling constants (i.e., leading, next-to-leading and next-to-next-to-leading logarithms). For the sake of this calculation we determined the beta function of the fermion-fermion-scalar-scalar interaction and the anomalous dimension of the scalar field. We shown that the improved effective potential provides a much more precise determination of the properties of the theory in the broken phase, compared to the standard effective potential obtained directly from the loop calculations. This happens because the region of the parameter space where dynamical symmetry breaking occurs is drastically reduced by the improvement discussed here.Comment: 29 pages, 10 figures, 1 tabl

Renormalization Group Improvement and Dynamical Breaking of Symmetry in a Supersymmetric Chern-Simons-matter Model

In this work, we investigate the consequences of the Renormalization Group Equation (RGE) in the determination of the effective superpotential and the study of Dynamical Symmetry Breaking (DSB) in an N = 1 supersymmetric theory including an Abelian Chern-Simons superfield coupled to N scalar superfields in (2+1) dimensional spacetime. The classical Lagrangian presents scale invariance, which is broken by radiative corrections to the effective superpotential. We calculate the effective superpotential up to two-loops by using the RGE and the beta functions and anomalous dimensions known in the literature. We then show how the RGE can be used to improve this calculation, by summing up properly defined series of leading logs (LL), next-to-leading logs (NLL) contributions, and so on... We conclude that even if the RGE improvement procedure can indeed be applied in a supersymmetric model, the effects of the consideration of the RGE are not so dramatic as it happens in the non-supersymmetric case.Comment: v4: 11 pages, 1 figure. Version accepted for publication in NP

Dynamical aspects of inextensible chains

In the present work the dynamics of a continuous inextensible chain is studied. The chain is regarded as a system of small particles subjected to constraints on their reciprocal distances. It is proposed a treatment of systems of this kind based on a set Langevin equations in which the noise is characterized by a non-gaussian probability distribution. The method is explained in the case of a freely hinged chain. In particular, the generating functional of the correlation functions of the relevant degrees of freedom which describe the conformations of this chain is derived. It is shown that in the continuous limit this generating functional coincides with a model of an inextensible chain previously discussed by one of the authors of this work. Next, the approach developed here is applied to a inextensible chain, called the freely jointed bar chain, in which the basic units are small extended objects. The generating functional of the freely jointed bar chain is constructed. It is shown that it differs profoundly from that of the freely hinged chain. Despite the differences, it is verified that in the continuous limit both generating functionals coincide as it is expected.Comment: 15 pages, LaTeX 2e + various packages, 3 figures. The title has been changed and three references have been added. A large part of the manuscript has been rewritten to improve readability. Chapter 4 has been added. It contains the construction of the generating functional without the shish-kebab approximation and a new derivation of the continuous limit of the freely jointed bar chai

On the validity of the adiabatic approximation in compact binary inspirals

Using a semi-analytical approach recently developed to model the tidal deformations of neutron stars in inspiralling compact binaries, we study the dynamical evolution of the tidal tensor, which we explicitly derive at second post-Newtonian order, and of the quadrupole tensor. Since we do not assume a priori that the quadrupole tensor is proportional to the tidal tensor, i.e. the so called "adiabatic approximation", our approach enables us to establish to which extent such approximation is reliable. We find that the ratio between the quadrupole and tidal tensors (i.e., the Love number) increases as the inspiral progresses, but this phenomenon only marginally affects the emitted gravitational waveform. We estimate the frequency range in which the tidal component of the gravitational signal is well described using the stationary phase approximation at next-to-leading post-Newtonian order, comparing different contributions to the tidal phase. We also derive a semi-analytical expression for the Love number, which reproduces within a few percentage points the results obtained so far by numerical integrations of the relativistic equations of stellar perturbations.Comment: 13 pages, 1 table, 2 figures. Minor changes to match the version appearing on Phys. Rev.

Chern-Simons Field Theories with Non-semisimple Gauge Group of Symmetry

Subject of this work is a class of Chern-Simons field theories with non-semisimple gauge group, which may well be considered as the most straightforward generalization of an Abelian Chern-Simons field theory. As a matter of fact these theories, which are characterized by a non-semisimple group of gauge symmetry, have cubic interactions like those of non-abelian Chern-Simons field theories, but are free from radiative corrections. Moreover, at the tree level in the perturbative expansion,there are only two connected tree diagrams, corresponding to the propagator and to the three vertex originating from the cubic interaction terms. For such theories it is derived here a set of BRST invariant observables, which lead to metric independent amplitudes. The vacuum expectation values of these observables can be computed exactly. From their expressions it is possible to isolate the Gauss linking number and an invariant of the Milnor type, which describes the topological relations among three or more closed curves.Comment: 16 pages, 1 figure, plain LaTeX + psfig.st