On the effective string spectrum of the tridimensional Z(2) gauge model

TL;DR

This study provides high-precision measurements of the string spectrum in 3D Z(2) gauge theory, confirming Nambu-Goto predictions at intermediate distances and revealing deviations at short distances due to additional effects.

Contribution

It offers the first detailed numerical comparison between the Z(2) gauge model's string spectrum and effective string theories, especially Nambu-Goto, at various distances.

Findings

Numerical data agrees with Nambu-Goto predictions at intermediate and large distances.

Data distinguishes between Nambu-Goto and free string models up to a certain distance.

Results support the breakdown of the effective string picture at short distances.

Abstract

We study the Z(2) lattice gauge theory in three dimensions, and present high precision estimates for the first few energy levels of the string spectrum. These results are obtained from new numerical data for the two-point Polyakov loop correlation function, which is measured in the 3d Ising spin system using duality. This allows us to perform a stringent comparison with the predictions of effective string models. We find a remarkable agreement between the numerical estimates and the Nambu-Goto predictions for the energy gaps at intermediate and large distances. The precision of our data allows to distinguish clearly between the predictions of the full Nambu-Goto action and the simple free string model up to an interquark distance $r \approx 10/\sqrt{\sigma}$. At the same time, our results also confirm the breakdown of the effective picture at short distances, supporting the hypothesis that terms which are not taken into account in the usual Nambu-Goto string formulation yield a non-trivial shift to the energy levels. Furthermore, we discuss the theoretical implications of these results.