Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry Protected Topological Superfluid $^3$He-B   Owing to the richness of symmetry and well-established knowledge on the bulk
superfluidity, the superfluid $^3$He has offered a prototypical system to study
intertwining of topology and symmetry. This article reviews recent progress in
understanding the topological superfluidity of $^3$He in a multifaceted manner,
including symmetry consideration, the Jackiw-Rebbi's index theorem, and the
quasiclassical theory. Special focus is placed on the symmetry protected
topological superfuidity of the $^3$He-B confined in a slab geometry. The
$^3$He-B under a magnetic field is separated to two different sub-phases: The
symmetry protected topological phase and non-topological phase. The former
phase is characterized by the existence of symmetry protected Majorana
fermions. The topological phase transition between them is triggered off by the
spontaneous breaking of a hidden discrete symmetry. The critical field is
quantitatively determined from the microscopic calculation that takes account
of magnetic dipole interaction of $^3$He nucleus. It is also demonstrated that
odd-frequency even-parity Cooper pair amplitudes are emergent in low-lying
quasiparticles. The key ingredients, symmetry protected Majorana fermions and
odd-frequency pairing, bring an important consequence that the coupling of the
surface states to an applied field is prohibited by the hidden discrete
symmetry, while the topological phase transition with the spontaneous symmetry
breaking is accompanied by anomalous enhancement and anisotropic quantum
criticality of surface spin susceptibility. We also illustrate common
topological features between topological crystalline superconductors and
symmetry protected topological superfluids, taking UPt$_3$ and Rashba
superconductors as examples.

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The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
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The categories of this paper are: stat
28
The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics