# The BRST-invariant vacuum state of the Gribov-Zwanziger theory

## TL;DR

This paper analyzes the effective action of the Gribov-Zwanziger theory, emphasizing BRST symmetry and renormalization, and demonstrates the stabilization of the vacuum through BRST-invariant condensates at one loop.

## Contribution

It introduces a BRST-invariant effective potential for the Gribov-Zwanziger theory, accounting for symmetry and renormalization, and explores vacuum stability at zero temperature.

## Key findings

- BRST-invariant dimension 2 condensates stabilize the vacuum
- Effective potential computed at one loop shows vacuum stabilization
- Framework established for finite temperature studies of the horizon condition

## Abstract

We revisit the effective action of the Gribov-Zwanziger theory, taking into due account the BRST symmetry and renormalization (group invariance) of the construction. We compute at one loop the effective potential, showing the emergence of BRST-invariant dimension 2 condensates stabilizing the vacuum. This paper sets the stage at zero temperature, and clears the way to studying the Gribov-Zwanziger gap equations, and particularly the horizon condition, at finite temperature in future work.