How Accurate is the Quantum String Bethe Ansatz?

TL;DR

This paper evaluates the precision of the quantum string Bethe ansatz by comparing its solutions with explicit one-loop calculations, confirming its accuracy for long strings and quantifying deviations for finite lengths.

Contribution

It provides a detailed comparison between the quantum string Bethe ansatz and explicit calculations, highlighting its exactness for infinite strings and quantifying finite-size deviations.

Findings

Bethe ansatz reproduces the spectrum of infinitely long strings exactly.

Deviations for finite strings are exponentially small in length.

The approach validates the Bethe ansatz as a reliable tool for string spectrum analysis.

Abstract

We compare solutions of the quantum string Bethe equations with explicit one-loop calculations in the sigma-model on AdS(5)xS(5). The Bethe ansatz exactly reproduces the spectrum of infinitely long strings. When the length is finite, we find that deviations from the exact answer arise which are exponentially small in the string length.