Speed limit in internal space of domain walls via all-order effective action of moduli motion

TL;DR

This paper derives an all-order effective action for internal moduli of domain walls, revealing a universal speed limit in their internal space, analogous to the speed of light, with potential implications for condensed matter physics.

Contribution

The authors develop a generic formula for the effective action of internal moduli in domain walls, demonstrating a universal internal speed limit across relativistic and non-relativistic theories.

Findings

Effective Lagrangian expressed as a function of Nambu-Goto Lagrangian

Existence of an internal speed limit in domain wall moduli space

Potential to observe the speed limit in condensed matter experiments

Abstract

We find that motion in internal moduli spaces of generic domain walls has an upper bound for its velocity. Our finding is based on our generic formula for all-order effective actions of internal moduli parameter of domain wall solitons. It is known that the Nambu-Goldstone mode $Z$ associated with spontaneous breaking of translation symmetry obeys a Nambu-Goto effective Lagrangian $\sqrt{1 - (\partial_0 Z)^2}$ detecting the speed of light ($|\partial_0 Z|=1$) in the target spacetime. Solitons can have internal moduli parameters as well, associated with a breaking of internal symmetries such as a phase rotation acting on a field. We obtain, for generic domain walls, an effective Lagrangian of the internal moduli $\epsilon$ to all order in $(\partial \epsilon)$. The Lagrangian is given by a function of the Nambu-Goto Lagrangian: $L = g(\sqrt{1 + (\partial_\mu \epsilon)^2})$. This shows generically the existence of an upper bound on $\partial_0 \epsilon$, i.e. a speed limit in the internal space. The speed limit exists even for solitons in some non-relativistic field theories, where we find that $\epsilon$ is a type I Nambu-Goldstone mode which also obeys a nonlinear dispersion to reach the speed limit. This offers a possibility of detecting the speed limit in condensed matter experiments.