# The effect of boundary conditions on dimensionally reduced field-theoretical models at finite temperature

## TL;DR

This paper investigates how different boundary conditions affect the process of dimensional reduction in finite-temperature field theories, revealing that boundary choices significantly influence the effective models and their properties.

## Contribution

It systematically analyzes the impact of various boundary conditions on dimensional reduction for both fermionic and bosonic models, highlighting new effects and distinctions.

## Key findings

- Boundary conditions alter the effective coupling in bosonic reduced models.
- Fermionic reduction yields models distinguishable from directly reduced lower-dimensional fermions.
- Antiperiodic boundary conditions prevent dimensional reduction altogether.

## Abstract

Here we understand \textit{dimensional reduction} as a procedure to obtain an effective model in $D-1$ dimensions that is related to the original model in $D$ dimensions. To explore this concept we use both a self-interacting fermionic model and self-interacting bosonic model. Furthermore, in both cases, we consider different boundary conditions in space: periodic, antiperiodic, Dirichlet and Neumann. For bosonic fields, we get the so defined dimensional reduction. Taking the simple example of a quartic interaction, we obtain that the boundary condition (periodic, Dirichlet, Neumann) influence the new coupling of the reduced model. For fermionic fields, we get the curious result that the model obtained reducing from $D$ dimensions to $D-1$ dimensions is distinguishable from taking into account a fermionic field originally in $D-1$ dimensions. Moreover, when one considers antiperiodic boundary condition in space (both for bosons or fermions) it is found that the dimensional reduction is not allowed.