39,203 research outputs found
Low-Energy Lorentz Invariance in Lifshitz Nonlinear Sigma Models
This work is dedicated to the study of both large- and perturbative
quantum behaviors of Lifshitz nonlinear sigma models with dynamical critical
exponent 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- 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
Supersymmetric Extension of the Quantum Spherical Model
In this work, we present a supersymmetric extension of the quantum spherical
model, both in components and also in the superspace formalisms. We find the
solution for short/long range interactions through the imaginary time formalism
path integral approach. The existence of critical points (classical and
quantum) is analyzed and the corresponding critical dimensions are determined.Comment: 21 pages, fixed notation to match published versio
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
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