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Title: 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 four-point 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 Chern-Simons-matter 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 non-perturbatively interpolate between SCFTs with M-theory 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 vector-like 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 low-lying CFT data for this theory.  more » « less
Award ID(s):
1820651
NSF-PAR ID:
10311730
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Journal of High Energy Physics
Volume:
2021
Issue:
5
ISSN:
1029-8479
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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