Effective theory of two-dimensional chiral superfluids: gauge duality and Newton-Cartan formulation

Abstract

We present a theory of Galilean-invariant conventional and chiral $p_x\pm i{p}_y$ fermionic superfluids at zero temperature in two spatial dimensions in terms of a dual gauge theory. Our formulation is general coordinate invariant. The parity-violating effects are encoded in the Wen-Zee term that gives rise to the Hall viscosity and edge current. We show that the relativistic superfluid with the Euler current reduces to the chiral superfluid in the limit $c\to \infty$. Using Newton-Cartan geometry we construct the covariant formulation of the effective theory and calculate the energy current.

v2: 15 pages, minor improvements, references added

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• Emergent geometry experienced by fermions in graphene in the presence of dislocations
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• Geometric Induction in Chiral Superfluids
• Hall viscosity and conductivity of two-dimensional chiral superconductors
• Hall viscosity in the A-phase of superfluid ${}^3$He
• Geometric and computational aspects of chiral topological quantum matter
• Universal nonlinear responses of quantum Hall systems with Galilean invariance
• Relativistic Gravity and Parity-Violating Non-Relativistic Effective Field Theories
• Hyperscaling violating Lifshitz holography
• Precise correspondence between the p-wave chiral superfluid and the spinless bosonic superfluid in the lowest Landau level
• Viscosities and shift in a chiral superfluid: a holographic study