# Comparison of 4d and 3d Lattice Results for the Electroweak Phase Transition

## TL;DR

This paper compares 4d and 3d lattice results for the electroweak phase transition, providing a non-perturbative check of dimensional reduction despite large uncertainties.

## Contribution

It offers the first direct comparison between 4d and 3d lattice results for the electroweak phase transition, testing the validity of dimensional reduction.

## Key findings

- Results are compatible within error margins.
- Provides evidence supporting dimensional reduction.
- Highlights limitations due to large error bars.

## Abstract

We compare 4d lattice results for the finite temperature phase transition in the SU(2)+Higgs model with 3d lattice results for the phase transition in the corresponding dimensionally reduced effective theory. While the large errorbars and the lack of a relation of the 4d lattice gauge coupling to continuum physics prevent rigorous conclusions, the results are nevertheless compatible. This provides a direct non-perturbative check of dimensional reduction in the present context.