Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable Gapless Bose Liquid Phases without any Symmetry   It is well-known that a stable algebraic spin liquid state (or equivalently
an algebraic Bose liquid (ABL) state) with emergent gapless photon excitations
can exist in quantum spin ice systems, or in a quantum dimer model on a
bipartite $3d$ lattice. This photon phase is stable against any weak
perturbation without assuming any symmetry. Further works concluded that
certain lattice models give rise to more exotic stable algebraic Bose liquid
phases with graviton-like excitations. In this paper we will show how these
algebraic Bose liquid states can be generalized to stable phases with even more
exotic types of gapless excitations and then argue that these new phases are
stable against weak perturbations. We also explicitly show that these theories
have an (algebraic) topological ground state degeneracy on a torus, and
construct the corresponding topological invariants.

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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an