# Constraint HMC algorithms for gauge-Higgs models

## TL;DR

This paper develops constraint Hybrid Monte Carlo algorithms for gauge-Higgs models, specifically SU(2) Gauge-Higgs Unification in five dimensions, to compare effective potentials across dimensions and understand phase properties.

## Contribution

It introduces new constraint HMC algorithms tailored for gauge-Higgs models to facilitate effective potential measurements and cross-dimensional analysis.

## Key findings

- Identification of regions with 4D adjoint or Abelian Higgs properties
- Comparison of effective potentials in 4D and 5D models
- Enhanced simulation techniques for gauge-Higgs phase studies

## Abstract

We present the construction of constraint HMC algorithms for gauge-Higgs models in order to measure the effective Higgs potential. In particular we focus on SU(2) Gauge-Higgs Unification models in five dimensions. Previous simulations have identified regions in the Higgs phase of these models which have properties of 4D adjoint or Abelian Higgs models. We want to test this relationship by comparing the effective potentials in five and four dimensions.