dc.contributor.author Walton, Edward dc.date.accessioned 2022-02-19T16:00:37Z dc.date.available 2022-02-19T16:00:37Z dc.date.issued 2022-02 dc.date.submitted 2021-07-30 dc.identifier.issn 1126-6708 dc.identifier.other jhep02(2022)155 dc.identifier.other 17840 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/334228 dc.description.abstract We provide evidence for conjectural dualities between nonrelativistic Chern-Simons-matter theories and theories of (fractional, nonAbelian) quantum Hall fluids in $2+1$ dimensions. At low temperatures, the dynamics of nonrelativistic Chern-Simons-matter theories can be described in terms of a nonrelativistic quantum mechanics of vortices. At critical coupling, this may be solved by geometric quantisation of the vortex moduli space. Using localisation techniques, we compute the Euler characteristic ${\chi}(\mathcal{L}^\lambda)$ of an arbitrary power $\lambda$ of a quantum line bundle $\mathcal{L}$ on the moduli space of vortices in $U(N_c)$ gauge theory with $N_f$ fundamental scalar flavours on an arbitrary closed Riemann surface. We conjecture that this is equal to the dimension of the Hilbert space of vortex states when the area of the metric on the spatial surface is sufficiently large. We find that the vortices in theories with $N_c = N_f = \lambda$ behave as fermions in the lowest nonAbelian Landau level, with strikingly simple quantum degeneracy. More generally, we find evidence that the quantum vortices may be regarded as composite objects, made of dual anyons. We comment on potential links between the dualities and three-dimensional mirror symmetry. We also compute the expected degeneracy of local Abelian vortices on the $\Omega$-deformed sphere, finding it to be a $q$-analog of the undeformed case. dc.language en dc.publisher Springer Science and Business Media LLC dc.subject Regular Article - Theoretical Physics dc.subject Chern-Simons Theories dc.subject Duality in Gauge Field Theories dc.subject Solitons Monopoles and Instantons dc.subject Differential and Algebraic Geometry dc.title Vortex counting and the quantum Hall effect dc.type Article dc.date.updated 2022-02-19T16:00:36Z prism.issueIdentifier 2 prism.publicationName Journal of High Energy Physics prism.volume 2022 dc.identifier.doi 10.17863/CAM.81641 dcterms.dateAccepted 2022-01-20 rioxxterms.versionofrecord 10.1007/JHEP02(2022)155 rioxxterms.version VoR rioxxterms.licenseref.uri http://creativecommons.org/licenses/by/4.0/ dc.contributor.orcid Walton, Edward [0000-0001-7609-0952] dc.identifier.eissn 1029-8479 cam.issuedOnline 2022-02-18 dc.identifier.arxiv 2107.14190
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