# QCD at finite temperature and partially negative flavour numbers

## TL;DR

This paper introduces a novel method for studying dynamical fermion effects in finite-temperature lattice QCD by extrapolating from negative flavour numbers, separating $Z_3$ breaking effects, and validating with simulations.

## Contribution

It presents a new approach using bermions to isolate $Z_3$ breaking contributions, enabling more efficient finite-temperature lattice QCD simulations.

## Key findings

- Results agree with hopping parameter expansion on $16^3\times 2$ lattice.
- Results agree with direct Monte Carlo simulations on $16^3\times 4$ lattice.
- Method effectively separates $Z_3$ breaking effects in fermion loop contributions.

## Abstract

We study dynamical fermion effects in lattice QCD at finite temperature. The method adopted is basically the extrapolation from negative flavour numbers already tested at zero temperature and based on the simulation of local bosonic theories, with an essential difference. With an appropriate choice of the boundary conditions on the bosonic fields, called ``bermions'', it is possible to separate the $Z_3$ breaking contribution of fermion loops to the effective action from the one conserving $Z_3$: the former is simulated exactly at a fixed positive and even flavour number, while the extrapolation from negative flavour numbers is made only on the $Z_3$ invariant part of the action. We test this approach by comparing our results on a $16^3\times 2$ lattice with those from a hopping parameter expansion and our results on a $16^3\times 4$ lattice with those of direct Monte Carlo simulations including the fermion determinant.