# Vacuum Stability and Symmetry Breaking in Left-Right Symmetric Model

## TL;DR

This paper establishes analytic criteria for vacuum stability and symmetry breaking in the left-right symmetric model, combining theoretical derivations with numerical validation and renormalization group analysis.

## Contribution

It introduces new analytic conditions for vacuum stability and symmetry breaking, enhancing understanding of the scalar potential in left-right symmetric models.

## Key findings

- Derived necessary and sufficient conditions for vacuum stability.
- Compared analytic conditions with numerical minimization results.
- Analyzed renormalization group evolution of scalar couplings.

## Abstract

We derive analytic necessary and sufficient conditions for the vacuum stability of the left-right symmetric model by using the concepts of copositivity and gauge orbit spaces. We also derive the conditions sufficient for successful symmetry breaking and the existence of a correct vacuum. We then compare results obtained from the derived conditions with those from numerical minimization of the scalar potential. Finally, we discuss the renormalization group analysis of the scalar quartic couplings through an example study that satisfies vacuum stability, perturbativity, unitarity and experimental bounds on the physical scalar masses.