Large N_c in chiral perturbation theory

The construction of the effective Lagrangian relevant for the mesonic sector of QCD in the large N_c limit meets with a few rather subtle problems. We thoroughly examine these and show that, if the variables of the effective theory are chosen suitably, the known large N_c counting rules of QCD can unambiguously be translated into corresponding counting rules for the effective coupling constants. As an application, we demonstrate that the Kaplan-Manohar transformation is in conflict with these rules and is suppressed to all orders in 1/N_c. The anomalous dimension of the axial singlet current generates an additional complication: The corresponding external field undergoes nonmultiplicative renormalization. As a consequence, the Wess-Zumino-Witten term, which accounts for the U(3)_R x U(3)_L anomalies in the framework of the effective theory, contains pieces that depend on the running scale of QCD. The effect only shows up at nonleading order in 1/N_c, but requires specific unnatural parity contributions in the effective Lagrangian that restore renormalization group invariance.Comment: 56 page

Driven collective instabilities in magneto-optical traps: a fluid-dynamical approach

We present a theoretical model to describe an instability mechanism in ultra-cold gases, where long-range interactions are taken into account. Focusing on the nonlinear coupling between the collective (plasma-like) and the center-of-mass modes, we show that the resulting dynamics is governed by a parametric equation of the generalized Mathieu type and compute the corresponding stability chart. We apply our model to typical ranges of magneto-optical traps (MOT) parameters and find a good agreement with previous experimental observations.Comment: 4 pages, 3 figures. Some minor changes in the published version

Inflationary paradigm after Planck 2013

Models of cosmic inflation posit an early phase of accelerated expansion of the universe, driven by the dynamics of one or more scalar fields in curved spacetime. Though detailed assumptions about fields and couplings vary across models, inflation makes specific, quantitative predictions for several observable quantities, such as the flatness parameter ($\Omega_k = 1 - \Omega$) and the spectral tilt of primordial curvature perturbations ($n_s - 1 = d \ln {\cal P}_{\cal R} / d \ln k$), among others---predictions that match the latest observations from the {\it Planck} satellite to very good precision. In the light of data from {\it Planck} as well as recent theoretical developments in the study of eternal inflation and the multiverse, we address recent criticisms of inflation by Ijjas, Steinhardt, and Loeb. We argue that their conclusions rest on several problematic assumptions, and we conclude that cosmic inflation is on a stronger footing than ever before.Comment: 11 pages, no figures; added references, and brief additions to Footnote 1, Section VI, and the Acknowledgment

Relativistic Corrections to Nonrelativistic Effective Field Theories

In this paper we develop a formalism for studying the nonrelativistic limit of relativistic field theories in a systematic way. By introducing a simple, nonlocal field redefinition, we transform a given relativistic theory, describing a real, self-interacting scalar field, into an equivalent theory, describing a complex scalar field that encodes at each time both the original field and its conjugate momentum. Our low-energy effective theory incorporates relativistic corrections to the kinetic energy as well as the backreaction of fast-oscillating terms on the behavior of the dominant, slowly varying component of the field. Possible applications of our new approach include axion dark matter, though the methods developed here should be applicable to the low-energy limits of other field theories as well.Comment: 31pp. References added, and 3 appendices added, showing (a) how to implement the field redefinition as a canonical transformation, (b) how to develop the effective field theory using a local field redefinition, and (c) how to use a further field redefinition to compare our results with those of Mukaida, Takimoto, and Yamad