# Vacuum misalignment in presence of four-Fermi operators

## TL;DR

This paper investigates how four-Fermi interactions can cause vacuum misalignment in strongly coupled gauge theories, emphasizing the importance of operator representations and potential lattice verification.

## Contribution

It analyzes the role of four-Fermi operators in vacuum misalignment, highlighting representation-dependent effects and providing insights relevant for phenomenological models.

## Key findings

- Interactions with different representations have varying signs affecting vacuum alignment
- Correct misalignment sign can be determined through lattice simulations
- Certain simple cases have predictable signs for vacuum misalignment

## Abstract

We consider the issue of vacuum misalignment induced by four-Fermi couplings in a generic strongly coupled four-dimensional gauge theory. After briefly reviewing the general formalism, we focus on the case of partial compositness-like operators at leading order, which is relevant in applications to phenomenology. We show that the interactions between an elementary fermion and composite spin-1/2 operators in various representations contribute to the effective potential with relative sign differences. Thus the correct sign required to misalign the vacuum is guaranteed to occur for some representations but not all of them. The overall sign dictating the specific representations responsible for misalignment can in principle be determined on the lattice. We also comment on the likely sign for some simple cases.