# Intertwined order and holography: the case of the parity breaking pair density wave

## TL;DR

This paper develops a holographic model that captures intertwined order phenomena, including pair density waves, by extending the Chern-Simons action to describe spontaneous symmetry breaking in a gravitational dual.

## Contribution

It introduces a minimal bottom-up holographic model with a Chern-Simons term that naturally produces pair density waves and spontaneous symmetry breaking of multiple orders.

## Key findings

- Constructed stationary inhomogeneous black hole solutions
- Demonstrated spontaneous breaking of U(1) and translational symmetry
- Provided a dual description of intertwined superconducting and parity orders

## Abstract

We present a minimal bottom-up extension of the Chern-Simons bulk action for holographic translational symmetry breaking that naturally gives rise to pair density waves. We construct stationary inhomogeneous black hole solutions in which both the U(1) symmetry and spatially translational symmetry are spontaneously broken at finite temperature and charge density. This novel solution provides a dual description of a superconducting phase intertwined with charge, current and parity orders.