# Fermi points and the Nambu sum rule in the polar phase of $^3$He

## TL;DR

This paper analyzes the polar phase of superfluid helium-3, showing how spin-orbit interactions transform a Fermi line into Fermi points and deriving the associated collective excitations and Nambu sum rule.

## Contribution

It demonstrates how spin-orbit interaction stabilizes Fermi points in the polar phase of $^3$He and calculates the gaps of collective bosonic states, establishing the Nambu sum rule.

## Key findings

- Spin-orbit interaction creates Fermi points from a Fermi line.
- Collective gapped bosonic states are identified and their gaps calculated.
- The Nambu sum rule relating these gaps is established.

## Abstract

We discuss the polar phase of $^3$He, which is realized in the anisotropic aerogel. We consider it in the framework of the BCS model. In the absence of the spin - orbit interaction this model predicts the appearance of the Fermi line. However, it is topologically unstable. We demonstrate, that the spin - orbit interaction gives rise to the appearance of the two Fermi points instead of the Fermi line. In addition to the gapless Nambu - Goldstone bosons in this system the collective gapped bosonic states exist. Their gaps are calculated, and the corresponding Nambu sum rule is established.