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.

arXiv commentv2: 15 pages, minor improvements, references added

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• Three-Dimensional Extended Newtonian (Super)Gravity
• New approach to nonrelativistic diffeomorphism invariance and its applications
• Torsional Newton-Cartan geometry from Galilean gauge theory
• Probing topological superconductors with emergent gravity
• The gravitational mass carried by sound waves
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• Emergent geometry experienced by fermions in graphene in the presence of dislocations
• Torsional Newton-Cartan Geometry and the Schrödinger Algebra
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• A Schrödinger approach to Newton-Cartan and Hořava-Lifshitz gravities
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• Geometric Induction in Chiral Superfluids
• On the question of symmetries in non-relativistic diffeomorphism invariant theories
• Scale Invariance in Newton-Cartan and Hořava-Lifshitz Gravity
• Milne boost from galilean gauge theory
• Hall viscosity and conductivity of two-dimensional chiral superconductors
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• Precise correspondence between the p-wave chiral superfluid and the spinless bosonic superfluid in the lowest Landau level
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