Spiky Phases of Smooth Membranes. Implications for Smooth Strings

TL;DR

This paper explores how smooth membranes can develop spike-like features when their curvature stiffness drops below critical levels, revealing phase transitions and potential implications for smooth strings in quantum chromodynamics.

Contribution

It introduces a mechanism for spike formation in membranes due to curvature stiffness changes, including phase transition descriptions and possible new phases.

Findings

Spike formation occurs via first-order or Kosterlitz-Thouless-like transitions.

Possible existence of hexagonal solid-like or liquid-like spike arrangements.

Implication of smooth strings between quarks.

Abstract

We point out a possible mechanism by which smooth surfaces can become spiky as the constant of curvature stiffness $\kappa$ falls below certain critical values. This happens either in a single first-order transition, or in a sequence of two Kosterlitz-Thouless-like transitions. There may also be additional phases in which the spikes form a hexagonal solid-like array or a disordered liquid-like structure. Our discussion suggests that there exist smooth strings between quarks.