# Type of dual superconductivity for the $SU(2)$ Yang--Mills theory

## TL;DR

This paper determines the type of dual superconductivity responsible for quark confinement in SU(2) Yang--Mills theory by solving field equations and fitting lattice simulation data, confirming it as type I and analyzing flux tube forces.

## Contribution

It provides a comprehensive solution for the vortex in the U(1) gauge-scalar model and refines the classification of dual superconductivity in SU(2) Yang--Mills theory as type I.

## Key findings

- Confirms type I dual superconductivity for quark confinement.
- Improves accuracy of the Ginzburg--Landau parameter estimation.
- Shows attractive forces among chromoelectric flux tubes.

## Abstract

We investigate the type of dual superconductivity responsible for quark confinement. For this purpose, we solve the field equations of the $U(1)$ gauge-scalar model to obtain the static vortex solution in the whole range without restricting to the long-distance region. Then we use the resulting magnetic field of the vortex to fit the gauge-invariant chromoelectric field connecting a pair of quark and antiquark which was measured by numerical simulations for $SU(2)$ Yang--Mills theory on a lattice. This result improves the accuracy of the fitted value for the Ginzburg--Landau parameter to reconfirm the type I dual superconductivity for quark confinement which was claimed by preceding works based on a fitting using the Clem ansatz. Moreover, we calculate the Maxwell stress tensor to obtain the distribution of the force around the flux tube. This result suggests that the attractive force acts among chromoelectric flux tubes, in agreement with the type I dual superconductivity.