Slow evolution of nearly-degenerate extremal surfaces

TL;DR

This paper investigates the slow evolution of nearly-degenerate extremal surfaces in the context of string theory in AdS spaces, linking tensionless string limits to integrable spin chains and renormalization group flows.

Contribution

It provides a detailed interpretation of the first order theory as the long-term evolution of tensionless strings perturbed by small tension, connecting geometric and field theory concepts.

Findings

Long-term evolution described by Hamiltonian flow on moduli space

Interpretation of the theory as a renormalization group flow

Connection between tensionless string limit and integrable spin chains

Abstract

It was conjectured recently that the string worldsheet theory for the fast moving string in AdS times a sphere becomes effectively first order in the time derivative and describes the continuous limit of an integrable spin chain. In this paper we will try to make this statement more precise. We interpret the first order theory as describing the long term evolution of the tensionless string perturbed by a small tension. The long term evolution is a Hamiltonian flow on the moduli space of periodic trajectories. It should correspond to the renormgroup flow on the field theory side.