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The spectrum of closed loops of fundamental flux in D = 3+1 SU(N) gauge theories

Andreas Athenodorou, Barak Bringoltz, Michael Teper

TL;DR

This study investigates the spectrum of closed flux tubes in D=3+1 SU(N) gauge theories using a variational lattice approach with ~700 operators, across SU(3) at two lattice spacings and SU(5). The authors compare the extracted energies to the Nambu-Goto (NG) model and various effective string theories (ESTs), finding that most states are well described by NG, even when tube lengths exceed the EST radius of convergence, suggesting a resummation of ESTs to NG. A handful of states with negative parity in the A1 representation exhibit large deviations from NG, hinting at deeper structure in the effective string description of large-N QCD strings. The results reinforce NG as a robust effective description for a broad range of flux-tube lengths and quantum numbers, while highlighting specific anomalous states that warrant further theoretical and lattice investigation, including massive excitations and open-string spectra.

Abstract

We study the spectrum of closed flux tubes in four dimensional SU(N) gauge theories. We do so by calculating the energies of the low lying states with the variational technique (whose basis consists of about ~700 operators). We study states of different values of angular momentum, transversal parity, longitudinal parity, and longitudinal momentum, and compare the results with effective string theories (ESTs) such as the Nambu-Goto (NG) model. Most of our states agree very well with the Nambu-Goto predictions and since most of our flux-tubes' lengths are outside the radius of convergence of the ESTs, then for some states it is only the NG that predicts the spectrum well. This strongly suggests that the ESTs can be re-summed. Nonetheless, there are a few states (all with negative parity and in the same representation of the lattice rotation group) that exhibit large deviations from the NG predictions; these deviations might provide clues to the nature of the effective string theory describing the large-N QCD string.

The spectrum of closed loops of fundamental flux in D = 3+1 SU(N) gauge theories

TL;DR

This study investigates the spectrum of closed flux tubes in D=3+1 SU(N) gauge theories using a variational lattice approach with ~700 operators, across SU(3) at two lattice spacings and SU(5). The authors compare the extracted energies to the Nambu-Goto (NG) model and various effective string theories (ESTs), finding that most states are well described by NG, even when tube lengths exceed the EST radius of convergence, suggesting a resummation of ESTs to NG. A handful of states with negative parity in the A1 representation exhibit large deviations from NG, hinting at deeper structure in the effective string description of large-N QCD strings. The results reinforce NG as a robust effective description for a broad range of flux-tube lengths and quantum numbers, while highlighting specific anomalous states that warrant further theoretical and lattice investigation, including massive excitations and open-string spectra.

Abstract

We study the spectrum of closed flux tubes in four dimensional SU(N) gauge theories. We do so by calculating the energies of the low lying states with the variational technique (whose basis consists of about ~700 operators). We study states of different values of angular momentum, transversal parity, longitudinal parity, and longitudinal momentum, and compare the results with effective string theories (ESTs) such as the Nambu-Goto (NG) model. Most of our states agree very well with the Nambu-Goto predictions and since most of our flux-tubes' lengths are outside the radius of convergence of the ESTs, then for some states it is only the NG that predicts the spectrum well. This strongly suggests that the ESTs can be re-summed. Nonetheless, there are a few states (all with negative parity and in the same representation of the lattice rotation group) that exhibit large deviations from the NG predictions; these deviations might provide clues to the nature of the effective string theory describing the large-N QCD string.

Paper Structure

This paper contains 10 sections, 3 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Setup of the lattice calculation
  3. Theoretical expectations for the spectrum from effective string theories
  4. The Nambu-Goto model
  5. Effective string theory approaches
  6. Results
  7. Ground states in the $q=0,1,2$ channels
  8. Further $q=0$ states
  9. Further $q=1$ states
  10. Summary

Figures (3)

  • Figure 1: Energies of the lightest states that correspond to $q=0,1,2$ NG ground states.
  • Figure 2: Energies of the four states with $q=0$ expected to be characterised by $n=1$.
  • Figure 3: Energies of the lightest five distinguishable states with $q=1$.