# Type of dual superconductivity for $SU(2)$ and $SU(3)$ Yang--Mills theories

## TL;DR

This paper determines the type of dual superconductivity in $SU(2)$ and $SU(3)$ Yang--Mills theories by solving the Abelian--Higgs model and fitting the results to lattice data, confirming the type I dual superconductivity responsible for quark confinement.

## Contribution

It provides a precise, gauge-invariant analysis of the dual superconductivity type in Yang--Mills theories using a full-range vortex solution and force distribution calculations.

## Key findings

- Confirms type I dual superconductivity for quark confinement.
- Improves accuracy of the Ginzburg--Landau parameter estimation.
- Shows attractive force distribution around the flux tube.

## Abstract

We investigate the type of dual superconductivity responsible for quark confinement. For this purpose, we solve the field equations of the $U(1)$ Abelian--Higgs 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 $SU(2)$ and $SU(3)$ Yang--Mills theories 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 an approximate method based on the Clem ansatz. Moreover, we calculate the Maxwell stress tensor for the fitted model to obtain the distribution of the force around the flux tube. This suggests that the attractive force acts on the surface perpendicular to the chromoelectric flux tube, in agreement with the type I dual superconductivity.