A Modern Approach to Superradiance

In this paper, we provide a simple and modern discussion of rotational superradiance based on quantum field theory. We work with an effective theory valid at scales much larger than the size of the spinning object responsible for superradiance. Within this framework, the probability of absorption by an object at rest completely determines the superradiant amplification rate when that same object is spinning. We first discuss in detail superradiant scattering of spin 0 particles with orbital angular momentum $\ell=1$, and then extend our analysis to higher values of orbital angular momentum and spin. Along the way, we provide a simple derivation of vacuum friction---a "quantum torque" acting on spinning objects in empty space. Our results apply not only to black holes but to arbitrary spinning objects. We also discuss superradiant instability due to formation of bound states and, as an illustration, we calculate the instability rate $\Gamma$ for bound states with massive spin 1 particles. For a black hole with mass $M$ and angular velocity $\Omega$, we find $\Gamma \sim (G M \mu)^7 \Omega$ when the particle's Compton wavelength $1/\mu$ is much greater than the size $GM$ of the spinning object. This rate is parametrically much larger than the instability rate for spin 0 particles, which scales like $(GM \mu)^9 \Omega$. This enhanced instability rate can be used to constrain the existence of ultralight particles beyond the Standard Model.Comment: 39 pages (v2 contains many added details and corrects an error in v1. In particular, the instability rates for leading vector bound states are computed exactly in the large Compton wavelength limit.

Zoology of condensed matter: Framids, ordinary stuff, extra-ordinary stuff

We classify condensed matter systems in terms of the spacetime symmetries they spontaneously break. In particular, we characterize condensed matter itself as any state in a Poincar\'e-invariant theory that spontaneously breaks Lorentz boosts while preserving at large distances some form of spatial translations, time-translations, and possibly spatial rotations. Surprisingly, the simplest, most minimal system achieving this symmetry breaking pattern---the "framid"---does not seem to be realized in Nature. Instead, Nature usually adopts a more cumbersome strategy: that of introducing internal translational symmetries---and possibly rotational ones---and of spontaneously breaking them along with their space-time counterparts, while preserving unbroken diagonal subgroups. This symmetry breaking pattern describes the infrared dynamics of ordinary solids, fluids, superfluids, and---if they exist---supersolids. A third, "extra-ordinary", possibility involves replacing these internal symmetries with other symmetries that do not commute with the Poincar\'e group, for instance the galileon symmetry, supersymmetry or gauge symmetries. Among these options, we pick the systems based on the galileon symmetry, the "galileids", for a more detailed study. Despite some similarity, all different patterns produce truly distinct physical systems with different observable properties. For instance, the low-energy $2\to 2$ scattering amplitudes for the Goldstone excitations in the cases of framids, solids and galileids scale respectively as $E^2$, $E^4$, and $E^6$. Similarly the energy momentum tensor in the ground state is "trivial" for framids ($\rho +p=0$), normal for solids ($\rho+p>0$) and even inhomogenous for galileids.Comment: 58 pages, 1 table, 1 free cut-and-paste project for rainy days in Appendi

Effective Field Theories in Cosmology

During the last 20 years, a large amount of detailed cosmological observations have promoted cosmology to the rank of high-precision science. Remarkably, all the observations currently available can be accounted for by assuming that (i) the universe is approximately homogeneous and isotropic on large scales, (ii) gravitational interactions are described by General Relativity with a non-vanishing cosmological constant and (ii) 85% of the matter content of the universe is in the form of dark matter, a presently unknown type of matter which interacts with ordinary matter only gravitationally. Current theoretical efforts are focused on gaining a deeper understanding of the small departures from perfect homogeneity and isotropy observed in our universe, the nature of dark matter and the physical origin of the cosmological constant. Effective field theory methods provide a natural framework to try to address such outstanding questions. For instance, such methods have been extensively used to study alternative theories of gravity which mimic a non-vanishing cosmological constant and to build models of the early universe which generate the observed anisotropies and inhomogeneities through a period of accelerated cosmic expansion. In this thesis, we study effective field theories of gravity which violate some basic tenets of General Relativity such as Lorentz invariance and the weak equivalence principle. We also employ effective field theory methods to explore the imprint that high energy physics can leave on the small departures from homogeneity and isotropy generated in the early universe

UV completion without symmetry restoration

We show that it is not possible to UV-complete certain low-energy effective theories with spontaneously broken space-time symmetries by embedding them into linear sigma models, that is, by adding "radial" modes and restoring the broken symmetries. When such a UV completion is not possible, one can still raise the cutoff up to arbitrarily higher energies by adding fields that transform non-linearly under the broken symmetries, that is, new Goldstone bosons. However, this (partial) UV completion does not necessarily restore any of the broken symmetries. We illustrate this point by considering a concrete example in which a combination of space-time and internal symmetries is broken down to a diagonal subgroup. Along the way, we clarify a recently proposed interpretation of inverse Higgs constraints as gauge-fixing conditions.Comment: 6 page

Effective string theory for vortex lines in fluids and superfluids

We discuss the effective string theory of vortex lines in ordinary fluids and low-temperature superfluids, by describing the bulk fluid flow in terms of a two-form field to which vortex lines can couple. We derive the most general low-energy effective Lagrangian that is compatible with (spontaneously broken) Poincare invariance and worldsheet reparameterization invariance. This generalizes the effective action developed by Lund and Regge and by Endlich and Nicolis. By applying standard field-theoretical techniques, we show that certain low-energy coupling constants -- most notably the string tension -- exhibit RG running already at the classical level. We discuss applications of our techniques to the study of Kelvin waves, vortex rings, and the coupling to bulk sound modes.Comment: 62 pages, 6 figure

Radiation of scalar modes and the classical double copy

The double copy procedure relates gauge and gravity theories through color-kinematics replacements and holds for both scattering amplitudes and in classical contexts. Moreover, it has been shown that there is a web of theories whose scattering amplitudes are related through operations that exchange color and kinematic factors. In this paper, we generalize and extend this procedure by showing that the classical perturbative double copy of pions corresponds to special Galileons. We consider point-particles coupled to the relevant scalar fields, and find the leading and next to leading order radiation amplitudes. By considering couplings motivated by those that would arise from extracting the longitudinal modes of the gauge and gravity theories, we are able to map the non-linear sigma model radiation to that of the special Galileon. We also construct the single copy by mapping the bi-adjoint scalar radiation to the non-linear sigma model radiation through generalized color-kinematics replacements.Comment: 30 pages, 5 figure