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The $(2,0)$ superconformal bootstrap

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arxiv 1507.05637 v1 pith:BBC72LO3 submitted 2015-07-20 hep-th

Christopher Beem , Madalena Lemos , Leonardo Rastelli , Balt C. van Rees This is my paper · ORCID
classification hep-th
keywords theorybootstrapboundscrossingdimensionsstresssuperconformaltensor
verification ladder T0 review T1 audit T2 compute T3 formal

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abstract

We develop the conformal bootstrap program for six-dimensional conformal field theories with $(2,0)$ supersymmetry, focusing on the universal four-point function of stress tensor multiplets. We review the solution of the superconformal Ward identities and describe the superconformal block decomposition of this correlator. We apply numerical bootstrap techniques to derive bounds on OPE coefficients and scaling dimensions from the constraints of crossing symmetry and unitarity. We also derive analytic results for the large spin spectrum using the lightcone expansion of the crossing equation. Our principal result is strong evidence that the $A_1$ theory realizes the minimal allowed central charge $(c=25)$ for any interacting $(2,0)$ theory. This implies that the full stress tensor four-point function of the $A_1$ theory is the unique unitary solution to the crossing symmetry equation at $c=25$. For this theory, we estimate the scaling dimensions of the lightest unprotected operators appearing in the stress tensor operator product expansion. We also find rigorous upper bounds for dimensions and OPE coefficients for a general interacting $(2,0)$ theory of central charge $c$. For large $c$, our bounds appear to be saturated by the holographic predictions obtained from eleven-dimensional supergravity.

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Cited by 5 Pith papers

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

    hep-th 2025-01 conditional novelty 7.0 of 10

    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.

  2. Bootstrapping 3D Conformal Field Theories with Product Analytic Functionals

    hep-th 2026-08 conditional novelty 6.5 of 10

    A bootstrap method using product analytic functionals gives stronger, faster-converging bounds in three-dimensional conformal field theory, including a new kink near external dimension 4.16.

  3. Superconformal Blocks for Mixed 1/2-BPS Correlators with $SU(2)$ R-symmetry

    hep-th 2019-08 conditional novelty 6.0 of 10

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

  4. Light cone OPE in a CFT with lowest twist scalar primary

    hep-th 2019-08 conditional novelty 5.0 of 10

    In a unitary CFT with a lowest-twist scalar primary, the scalar contributes to the lightcone OPE only at subleading order, and no positive averaged operator analogous to the ANEC exists for a scalar integral.

  5. Chiral algebra correlators of the $6$d, $\mathcal{N}=(2,0)$ theory with a defect

    hep-th 2025-06 conditional novelty 4.0 of 10

    A chiral-algebra bootstrap reproduces the defect two-point correlators of the 6d (2,0) theory using only bulk-channel data and predicts new defect-channel OPE coefficients.

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