Abstract
We analyze exactly marginal deformations of 3d \( \mathcal{N} \) = 4 Lagrangian gauge theories, especially mixed-branch operators with both electric and magnetic charges. These mixed-branch moduli can either belong to products of electric and magnetic current supermultiplets, or be single-trace (non-factorizable). Apart from some exceptional quivers that have additional moduli, 3d \( \mathcal{N} \) = 4 theories described by genus g quivers with nonabelian unitary gauge groups have exactly g single-trace mixed moduli, which preserve the global flavour symmetries. This partly explains why only linear and circular quivers have known AdS4 supergravity duals. Indeed, for g > 1, AdS4 gauged supergravities cannot capture the entire g-dimensional moduli space even if one takes into account the quantization moduli of boundary conditions. Likewise, in a general Lagrangian theory, we establish (using the superconformal index) that the number of single-trace mixed moduli is bounded below by the genus of a graph encoding how nonabelian gauge groups act on hypermultiplets.
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Acknowledgments
We thank Costas Bachas for a closely related collaboration and discussions, and Antoine Bourget for useful comments and examples. B.L.F. was employed by the Institut Philippe Meyer (École Normale Supérieure, Paris, France) for a large proportion of the work. I.L. is supported by the Deutsche Forschungsgemeinschaft under Germany’s Excellence Strategy — EXC-2094 – 390783311 (the ORIGINS Excellence Cluster). I.L. thanks the LPENS and LPTHE for the hospitality during the final stages of this work.
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Lavdas, I., Le Floch, B. Mixed moduli in 3d \( \mathcal{N} \) = 4 higher-genus quivers. J. High Energ. Phys. 2023, 124 (2023). https://doi.org/10.1007/JHEP05(2023)124
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DOI: https://doi.org/10.1007/JHEP05(2023)124