Low-Energy Lorentz Invariance in Lifshitz Nonlinear Sigma Models

This work is dedicated to the study of both large-$N$ and perturbative quantum behaviors of Lifshitz nonlinear sigma models with dynamical critical exponent $z=2$ in 2+1 dimensions. We discuss renormalization and renormalization group aspects with emphasis on the possibility of emergence of Lorentz invariance at low energies. Contrarily to the perturbative expansion, where in general the Lorentz symmetry restoration is delicate and may depend on stringent fine-tuning, our results provide a more favorable scenario in the large-$N$ framework. We also consider supersymmetric extension in this nonrelativistic situation.Comment: 28 pages, 4 figures, minor clarifications, typos corrected, published versio

Lorentz Invariance in Shape Dynamics

Shape dynamics is a reframing of canonical general relativity in which time reparametrization invariance is "traded" for a local conformal invariance. We explore the emergence of Lorentz invariance in this model in three contexts: as a maximal symmetry, an asymptotic symmetry, and a local invariance.Comment: v2: discussion of light cone structure added; minor typos fixed; 14 page

On Ward Identities in Lifshitz-like Field Theories

In this work, we develop a normal product algorithm suitable to the study of anisotropic field theories in flat space, apply it to construct the symmetries generators and describe how their possible anomalies may be found. In particular, we discuss the dilatation anomaly in a scalar model with critical exponent z=2 in six spatial dimensions.Comment: Clarifications adde

Mean Field Limits for Interacting Diffusions in a Two-Scale Potential

In this paper we study the combined mean field and homogenization limits for a system of weakly interacting diffusions moving in a two-scale, locally periodic confining potential, of the form considered in~\cite{DuncanPavliotis2016}. We show that, although the mean field and homogenization limits commute for finite times, they do not, in general, commute in the long time limit. In particular, the bifurcation diagrams for the stationary states can be different depending on the order with which we take the two limits. Furthermore, we construct the bifurcation diagram for the stationary McKean-Vlasov equation in a two-scale potential, before passing to the homogenization limit, and we analyze the effect of the multiple local minima in the confining potential on the number and the stability of stationary solutions

Beliefs and actions in the trust game: creating instrumental variables to estimate the causal effect

In many economic contexts, an elusive variable of interest is the agent's expectation about relevant events, e.g. about other agents' behavior. Recent experimental studies as well as surveys have asked participants to state their beliefs explicitly, but little is known about the causal relation between beliefs and other behavioral variables. This paper discusses the possibility of creating exogenous instrumental variables for belief statements, by shifting the probabilities of the relevant events. We conduct trust game experiments where the amount sent back by the second player (trustee) is exogenously varied by a random process, in a way that informs only the �first player (trustor) about the realized variation. The procedure allows detecting causal links from beliefs to actions under plausible assumptions. The IV estimates indicate a signi�ficant causal effect, comparable to the connection between beliefs and actions that is suggested by OLS analyses

Constraining strangeness in dense matter with GW170817

Particles with strangeness content are predicted to populate dense matter, modifying the equation of state of matter inside neutron stars as well as their structure and evolution. In this work, we show how the modeling of strangeness content in dense matter affects the properties of isolated neutrons stars and the tidal deformation in binary systems. For describing nucleonic and hyperonic stars we use the many-body forces model (MBF) at zero temperature, including the $\phi$ mesons for the description of repulsive hyperon-hyperon interactions. Hybrid stars are modeled using the MIT Bag Model with vector interaction (vMIT) in both Gibbs and Maxwell constructions, for different values of bag constant and vector interaction couplings. A parametrization with a Maxwell construction, which gives rise to third family of compact stars (twin stars), is also investigated. We calculate the tidal contribution that adds to the post-Newtonian point-particle corrections, the associated love number for sequences of stars of different composition (nucleonic, hyperonic, hybrid and twin stars), and determine signatures of the phase transition on the gravitational waves in the accumulated phase correction during the inspirals among different scenarios for binary systems. On the light of the recent results from GW170817 and the implications for the radius of $\sim1.4\,\mathrm{M_{\odot}}$ stars, our results show that hybrid stars can only exist if a phase transition takes place at low densities close to saturation