Spiky strings in Bethe Ansatz at strong coupling

TL;DR

This paper constructs explicit two-cut Bethe Ansatz solutions for spiky strings in AdS3 x S1 at strong coupling, matching classical string results and revealing new scaling behaviors at large spins and winding numbers.

Contribution

It introduces asymmetric Bethe root distributions for spiky strings and derives a novel scaling limit for their energy at high spins and winding.

Findings

Constructed explicit two-cut solutions matching classical results.

Discovered a new energy scaling law at large spins and winding.

Extended known scaling laws for folded spinning strings.

Abstract

We study spiky string solutions in AdS3 x S1 that are characterized by two spins S,J as well as winding m in S1 and spike number n. We construct explicitly two-cut solutions by using the SL(2) asymptotic Bethe Ansatz equations at leading order in strong coupling. Unlike the folded spinning string, these solutions have asymmetric distributions of Bethe roots. The solutions match the known spiky string classical results obtained directly from string theory for arbitrary semiclassical parameters, including J=0 and any value of S, namely short and long strings. At large spins and winding number the string touches the boundary, and we find a new scaling limit with the energy given as E-S = n /2/ pi sqrt[1+ 4 pi^2/n^2 (J^2/ln^2 S + m^2/ln^2 S)] ln S. This is a generalization of the known scaling for the folded spinning string.