# Field Strength and Monopoles in Dual U(1) Lattice Gauge Theory

## TL;DR

This paper explores duality transformations in Abelian U(1) lattice gauge theories, enabling more efficient calculations of confinement-related observables and providing insights into monopole behavior and dual superconductor models.

## Contribution

It demonstrates duality transformations for correlation functions in U(1) lattice gauge theories and applies this to analyze monopoles and the dual superconductor model.

## Key findings

- Duality simplifies expectation value calculations in the confinement phase.
- The dual theory can be viewed as a limit of a dual non-compact Abelian Higgs model.
- Applications for simulating dual U(1) gauge theories are presented.

## Abstract

In any Abelian gauge theory with an action periodic in the link variables one can perform a duality transformation not only in the partition function, but also in correlation functions including Polyakov loops. The calculation of expectation values in the confinement phase, like electric field strength or monopole currents in the presence of external charges, becomes significantly more efficient simulating the dual theory. We demonstrate this using the ordinary Wilson action. This approach also allows a quantitative analysis of the dual superconductor model, because the dual transformed U(1) theory can be regarded as limit of a dual non-compact Abelian Higgs model. In this way we also try to interpret the behaviour of monopole condensate and string fluctuations. Finally we present some applications for simulating the dual U(1) gauge theory.