Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fermion condensation and super pivotal categories   We study fermionic topological phases using the technique of fermion
condensation. We give a prescription for performing fermion condensation in
bosonic topological phases which contain a fermion. Our approach to fermion
condensation can roughly be understood as coupling the parent bosonic
topological phase to a phase of physical fermions, and condensing pairs of
physical and emergent fermions. There are two distinct types of objects in
fermionic theories, which we call "m-type" and "q-type" particles. The
endomorphism algebras of q-type particles are complex Clifford algebras, and
they have no analogues in bosonic theories. We construct a fermionic
generalization of the tube category, which allows us to compute the
quasiparticle excitations in fermionic topological phases. We then prove a
series of results relating data in condensed theories to data in their parent
theories; for example, if $\mathcal{C}$ is a modular tensor category containing
a fermion, then the tube category of the condensed theory satisfies
$\textbf{Tube}(\mathcal{C}/\psi) \cong \mathcal{C} \times (\mathcal{C}/\psi)$.
We also study how modular transformations, fusion rules, and coherence
relations are modified in the fermionic setting, prove a fermionic version of
the Verlinde dimension formula, construct a commuting projector lattice
Hamiltonian for fermionic theories, and write down a fermionic version of the
Turaev-Viro-Barrett-Westbury state sum. A large portion of this work is devoted
to three detailed examples of performing fermion condensation to produce
fermionic topological phases: we condense fermions in the Ising theory, the
$SO(3)_6$ theory, and the $\frac{1}{2}\text{E}_6$ theory, and compute the
quasiparticle excitation spectrum in each of these examples.

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The categories of this paper are: supr-con
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
1
The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org