# Boundary central charge from bulk odd viscosity - chiral superfluids

## TL;DR

This paper develops a low energy effective field theory for chiral superfluids, revealing how the boundary chiral central charge influences bulk odd viscosity and proposing measurable bulk observables for its detection.

## Contribution

It introduces a novel effective field theory linking boundary chiral central charge to bulk odd viscosity in superfluids, with practical measurement proposals.

## Key findings

- Odd viscosity depends on boundary chiral central charge.
- Bulk observables can measure the boundary chiral central charge.
- Effective theory matches microscopic model calculations.

## Abstract

We derive a low energy effective field theory for chiral superfluids, which accounts for both spontaneous symmetry breaking and fermionic ground-state topology. Using the theory, we show that the odd (or Hall) viscosity tensor, at small wave-vector, contains a dependence on the chiral central charge $c$ of the boundary degrees of freedom, as well as additional non-universal contributions. We identify related bulk observables which allow for a bulk measurement of $c$. In Galilean invariant superfluids, only the particle current and density responses to strain and electromagnetic fields are required. To complement our results, the effective theory is benchmarked against a perturbative computation within a canonical microscopic model.