Abstract
In this work, a second-order transport coefficient (the curvature-matter coupling $\kappa$) is calculated exactly for the 3+1d O(N) model at large N for any coupling value. Since the theory is `trivial' in the sense of possessing a Landau pole, the result for $\kappa$ only is free from cut-off artifacts much below the Landau pole in the effective field theory sense. Nevertheless, this leaves a large range of coupling values where this transport coefficient can be determined non-perturbatively and analytically with little ambiguity. Along with thermodyamic results also calculated in this work, I expect exact large N results to provide good quantitative predictions for N=1 scalar field theory with $\phi^4$ interaction.
Highlights
Transport coefficients determine the real-time relaxation of a perturbation around a state of equilibrium
There are nonlinear corrections which come with their own respective transport coefficients
There are different types of perturbations (“channels”) which predominately couple to different combinations of transport coefficients, for instance the sound channel and the shear channel
Summary
Transport coefficients determine the real-time relaxation of a perturbation around a state of equilibrium. For the purpose of this work, I will consider the somewhat exotic transport coefficient κ, which appears as a second-order correction in the familiar sound and shear mode channels and which was introduced in Refs. Into the description of relativistic fluid as the leading-order correction when considering the coupling of matter to perturbations in the curvature of space-time (e.g., gravitational waves). Since the Ricci tensor is second order in a gradient expansion, this shows that κ is the leadingorder transport coefficient for gravity-matter perturbations. Because of relations similar in nature to the Einstein relations for diffusion, this curvature-matter coupling coefficient κ enters in the real-time evolution of sound waves in flat space-time (albeit as a correction to first-order transport governed by shear and bulk viscosity). Sensitivity to the cutoff scale can be tested for by varying the renormalization scale parameter, providing a quantitative handle on the breakdown of the theory
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
