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A superfluid spontaneously breaks the usual $U(1)$ symmetry because ofcondensation. In this article, we illustrate six classes of emergent $U(1)$symmetries naturally appear in infrared limits in a broad class of gaplesstopological superfluids (that either belong to a stable phase or are quantumcritical). In gapless states we have considered, emergent $U(1)$ symmetrygroups are embedded in an $Spin(4)=SU(2) \otimes SU(2)$ group that arealgebraically isomorphic to an $SO(4)$ group. All $U(1)$ charges associatedwith symmetries are further invariant under an $SU(2)$ spin group or anequivalent of it but always break pre-existing higher space-time Lorentzsymmetry of $SO(3,1)$ group. Emergent $U(1)$ symmetries can be furtherspontaneously broken only if interactions are strong enough and resultantstrong coupling states become fully gapped. However if states remain gapless,emergent $U(1)$ symmetries are always present, despite that these states mayexhibit much lower space-time symmetries compared to their weakly interactinggapless Lorentz symmetric counter parts. In the limit of our interests, we haveidentified all possible gapless real fermions with or without Lorentzsymmetries and find that they all display emergent $U(1)$ symmetries in theinfrared limit.We argue emergent $U(1)$ symmetries in infrared are intrinsic ina broad class of interacting gapless superfluid or superconducting states andare typically well defined in high dimensions where there are infrared stablefixed points dictating emergent properties.

Emergent $U(1)$ Symmetries and $\tau$-$\sigma$ Duality in Gapless Superfluids or Superconductors