A bstract We introduce a systematic approach to constructing $$ \mathcal{N} $$ N = 1 Lagrangians for a class of interacting $$ \mathcal{N} $$ N = 2 SCFTs. We analyse in detail the simplest case of the construction, arising from placing branes at an orientifolded ℂ 2 / ℤ 2 singularity. In this way we obtain Lagrangian descriptions for all the R 2 ,k theories. The rank one theories in this class are the E 6 MinahanNemeschansky theory and the C 2 × U(1) ArgyresWittig theory. The Lagrangians that arise from our brane construction manifestly exhibit either the entire expected flavour symmetry group of the SCFT (for even k ) or a fullrank subgroup thereof (for odd k ), so we can compute the full superconformal index of the $$ \mathcal{N} $$ N = 2 SCFTs, and also systematically identify the Higgsings associated to partial closing of punctures.
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The 3d $$ \mathcal{N} $$ = 6 bootstrap: from higher spins to strings to membranes
A bstract We study the space of 3d $$ \mathcal{N} $$ N = 6 SCFTs by combining numerical bootstrap techniques with exact results derived using supersymmetric localization. First we derive the superconformal block decomposition of the fourpoint function of the stress tensor multiplet superconformal primary. We then use supersymmetric localization results for the $$ \mathcal{N} $$ N = 6 U( N ) k × U( N + M ) −k ChernSimonsmatter theories to determine two protected OPE coefficients for many values of N, M, k . These two exact inputs are combined with the numerical bootstrap to compute precise rigorous islands for a wide range of N, k at M = 0, so that we can nonperturbatively interpolate between SCFTs with Mtheory duals at small k and string theory duals at large k . We also present evidence that the localization results for the U(1) 2 M × U (1 + M ) − 2 M theory, which has a vectorlike large M limit dual to higher spin theory, saturates the bootstrap bounds for certain protected CFT data. The extremal functional allows us to then conjecturally reconstruct lowlying CFT data for this theory.
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 Award ID(s):
 1820651
 NSFPAR ID:
 10311730
 Date Published:
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2021
 Issue:
 5
 ISSN:
 10298479
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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