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This is a Quantitative Study study.

September 28, 2025Open Access

Decomposition in 2d non-invertible gaugings

Key Points

Decomposition theory for 2D quantum field theories is extended to include gauged Rep(H) symmetry co-occurring with finite groups.
Explicit computation of partition functions confirmed previous results, indicating a consistent framework for gauged symmetries.
The approach paves the way for conjecturing decompositions in more general cases involving various Hopf algebras.
Findings contribute to understanding category theory in quantum field theories and suggest avenues for future research on symmetries.

Abstract

We extend decomposition to 2d QFT's with a gauged Rep (H) symmetry category for H a finite-dimensional semisimple Hopf algebra with Rep (G) trivially-acting and Vec () the remaining symmetry, for G, finite groups. We check our extension by explicitly computing partition functions, and by verifying that previous results arise as special cases. Then, drawing from these computations, we formulate a plausible decomposition conjecture for the even more general case of Rep (H'') trivially-acting and Rep (H') the remaining symmetry, for H', H'' Hopf algebras, not necessarily associated with groups.

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Alonso Perez-Lona (Mon,) studied this question.

synapsesocial.com/papers/68d90a0f41e1c178a14f6ac2 https://doi.org/https://doi.org/10.48550/arxiv.2503.07727

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