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dc.contributor.authorWalton, Edward
dc.date.accessioned2022-05-27T16:08:23Z
dc.date.available2022-05-27T16:08:23Z
dc.date.issued2021-07-29
dc.date.submitted2021-07-30
dc.identifier.issn1126-6708
dc.identifier.otherjhep02(2022)155
dc.identifier.other17840
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/337553
dc.description.abstractWe 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.languageen
dc.publisherSpringer Science and Business Media LLC
dc.subjectRegular Article - Theoretical Physics
dc.subjectChern-Simons Theories
dc.subjectDuality in Gauge Field Theories
dc.subjectSolitons Monopoles and Instantons
dc.subjectDifferential and Algebraic Geometry
dc.titleVortex counting and the quantum Hall effect
dc.typeArticle
dc.date.updated2022-05-27T16:08:22Z
prism.issueIdentifier2
prism.publicationNameJournal of High Energy Physics
prism.volume2022
dc.identifier.doi10.17863/CAM.84962
dcterms.dateAccepted2022-01-20
rioxxterms.versionofrecord10.1007/jhep02(2022)155
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0/
dc.contributor.orcidWalton, Edward [0000-0001-7609-0952]
dc.identifier.eissn1029-8479
cam.issuedOnline2022-02-18
dc.identifier.arxiv2107.14190


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