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Top Down Approach to 6D SCFTs

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arxiv 1805.06467 v5 pith:24IUKSIK submitted 2018-05-16 hep-th math.AGmath.RT

Jonathan J. Heckman , Tom Rudelius This is my paper · ORCID
classification hep-thmath.AGmath.RT
keywords theoriesfieldscftsquantumarticledownexplaininclude
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Six-dimensional superconformal field theories (6D SCFTs) occupy a central place in the study of quantum field theories encountered in high energy theory. This article reviews the top down construction and study of this rich class of quantum field theories, in particular, how they are realized by suitable backgrounds in string / M- / F-theory. We review the recent F-theoretic classification of 6D SCFTs, explain how to calculate physical quantities of interest such as the anomaly polynomial of 6D SCFTs, and also explain recent progress in understanding renormalization group flows for deformations of such theories. Additional topics covered by this review include some discussion on the (weighted and signed) counting of states in these theories via superconformal indices. We also include several previously unpublished results as well as a new variant on the swampland conjecture for general quantum field theories decoupled from gravity. The aim of the article is to provide a point of entry into this growing literature rather than an exhaustive overview.

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Cited by 6 Pith papers

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  1. Cobordism Utopia: U-Dualities, Bordisms, and the Swampland

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    For 8d maximal supergravity, the spin bordism groups Omega_k^Spin(B(SL(2,Z) x SL(3,Z))) for k=1..7 are computed and each generator is realized by a string/M/F-theory background, some of which are non-geometric.

  2. Anomaly Matching in 6d $\mathcal{N}=(2,0)$ SCFTs from M5 Cobordism

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    M5 bordism classifies the invertible phases of 6d (2,0) anomaly theories, and the Hopf-Wess-Zumino term is the phase that transgresses to the second Pontryagin class.

  3. The Higgs Mechanism -- Hasse Diagrams for Symplectic Singularities

    hep-th 2019-08 conditional novelty 7.0 of 10

    Partial Higgsing patterns of supersymmetric gauge theories match the Hasse diagrams of symplectic leaf closures of their Higgs branches, and these diagrams can be computed using magnetic quivers and quiver subtraction.

  4. A Pathway to Decay and Fission of Orthosymplectic Quiver Theories

    hep-th 2024-12 conditional novelty 6.0 of 10

    An orthosymplectic extension of the Decay and Fission algorithm is proposed, validated on class S and 6d orbi-instanton quivers, and used to predict new Higgs branch RG flows.

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    Explicit superconformal blocks for mixed half-BPS correlators with SU(2) R-symmetry are computed for all contributing multiplets in a dimension-independent way.

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    Pedagogical crash-course notes on supersymmetric field theory across 2–10 dimensions, organized around recurring structures such as holomorphy, dualities, indices, BPS data, and anomalies.

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