We propose a geometric description of all gapped excitations in fractional quantum Hall phases that reveals several fundamental understandings with experimental consequences. These include a duality between the Hilbert space of multiple gapped “gravitonlike” spin 2 excitations at $\nu =1/3$ Laughlin phase, and that of non-Abelian quasiholes of an irrational Haffnian conformal field theory. This leads us to construct microscopic wave functions for multiple higher-spin gapped neutral modes in the Laughlin phase. Carrying spin $s\ge 2$, they emerge from higher-order geometric deformations of the topological ground state, and live within the Gaffnian conformal Hilbert space asymptotically. We show that the full many-body Hilbert space of a fractional quantum Hall phase can be generated from superpositions of such geometric deformations, supporting a concrete geometric interpretation of all gapped excitations. We analyze the scattering between these higher-spin modes and conjecture that they can have long lifetimes, and propose methods for their experimental detection.

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• Fractional quantum Hall effect
• Geometric & topological phases
• Quasiparticles & collective excitations
• Gravitons