Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Nambu's Fermion-Boson Relations for Superfluid $^3$He-B   Superfluid $^3$He is a spin-triplet ($S=1$), p-wave ($L=1$) BCS condensate of
Cooper pairs with total angular momentum $J=0$ in the ground state. In addition
to the breaking of $U(1)$ gauge symmetry, separate spin or orbital rotation
symmetry is broken to the maximal sub-group, $SO(3)_S\times SO(3)_L\rightarrow
SO(3)_J$. The Fermions acquire mass, $m_F\equiv\Delta$, where $\Delta$ is the
BCS gap. There are also 18 Bosonic excitations - 4 Nambu-Goldstone (NG) modes
and 14 massive amplitude Higgs (AH) modes. The Bosonic modes are labelled by
the total angular momentum, $J\in\{0,1,2\}$, and parity under particle-hole
symmetry, $C=\pm 1$. For each pair of angular momentum quantum numbers,
$J,J_z$, there are two Bosonic partners with $C=\pm 1$. Based this spectrum
Nambu proposed a sum rule connecting the Fermion and Boson masses for BCS type
theories, which for $^3$He-B is $M_{J^+}^2 + M_{J^-}^2 = 4m_F^2$ for each
family of Bosonic modes labelled by $J$, where $M_{J^C}$ is the mass of the
Bosonic mode with quantum numbers $(J,C)$. Nambu's sum rule (NSR) has recently
been discussed in the context of Nambu-Jona-Lasinio models for physics beyond
the standard model to speculate on possible partners to the recently discovered
Higgs Boson at higher energies. Here we point out that Nambu's Fermion-Boson
mass relations are not exact. Corrections to the Bosonic masses from (i)
leading order strong-coupling corrections to BCS theory, and (ii) polarization
of the parent Fermionic vacuum lead to violations of the sum-rule. Results for
these mass corrections are given in both the $T\rightarrow 0$ and $T\rightarrow
T_c$ limits. We also discuss experimental results, and theoretical analysis,
for the masses of the $J^{C}=2^{\pm}$ Higgs modes and the magnitude of the
violation of the NSR.

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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: math