Exact correlators of BPS Operators from the 3d superconformal bootstrap

By Shai M. Chester, Jaehoon Lee, Silviu S. Pufu, Ran Yacoby. 2014

151 citations recorded by the source corpus.

A bstractWe use the superconformal bootstrap to derive exact relations between OPE coefficients in three-dimensional superconformal field theories with N≥4$$ \mathcal{N}\ge 4 $$ supersymmetry. These relations follow from a consistent truncation of the crossing symmetry equations that is associated with the cohomology of a certain supercharge. In N=4$$ \mathcal{N}=4 $$ SCFTs, the non-trivial cohomology classes are in one-to-one correspondence with certain half-BPS operators, provided that these operators are restricted to lie on a line. The relations we find are powerful enough to allow us to determine an infinite number of OPE coefficients in the interacting SCFT (U(2)2× U(1)−2 ABJ theory) that constitutes the IR limit of O(3) N=8$$ \mathcal{N}=8 $$ super-Yang-Mills theory. More generally, in N=8$$ \mathcal{N}=8 $$ SCFTs with a unique stress tensor, we are led to conjecture that many superconformal multiplets allowed by group theory must actually be absent from the spectrum, and we test this conjecture in known N=8$$ \mathcal{N}=8 $$ SCFTs using the superconformal index. For generic N=8$$ \mathcal{N}=8 $$ SCFTs, we also improve on numerical bootstrap bounds on OPE coefficients of short and semi-short multiplets and discuss their relation to the exact relations between OPE coefficients we derived. In particular, we show that the kink previously observed in these bounds arises from the disappearance of a certain quarter-BPS multiplet, and that the location of the kink is likely tied to the existence of the U(2)2× U(1)−2 AJ theory, which can be argued to not possess this multiplet.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3f7d660b80f6fe1d986af5341a9741d65ec6a40d

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Citations in the corpus

TASI Lectures on the Conformal Bootstrap (2016, background): “) • What protected information can be computed using supersymmetry? Bootstrap studies recently led to the discovery of beautiful new algebraic structures in the OPE algebra of supersymmetric theories in 3, 4, 6 dimensions [82, 107, 108].”
Bootstrapping SCFTs with four supercharges (2015, unknown): “This feature was further explored to great efficacy in six [21], four [22, 23] and three dimensions [24].”
The (2, 0) superconformal bootstrap (2015, methodology): “This is a huge simplification in bootstrap studies and has already been exploited for maximally superconformal field theories in four [62] and three [83,84] dimensions.”
$$ \mathcal{N} $$ = 4 Super-Yang-Mills correlators at strong coupling from string theory and localization (2019, methodology): “ves of the N= 1 partition function on S4, for which an expression was proposed in [47]. 27In 3d, rst steps of this kind were taken for the maximally supersymmetric ABJM theory, where bootstrap bounds [65,88] have been successfully matched to both localization [89] and large NMellin space calculation”
Bootstrapping 3D fermions (2015, methodology): “The numerical bootstrap has been applied to such cases in [11–16].”
Bootstrapping the O(N) archipelago (2015, unknown): “In recent years great progress has been made in the conformal bootstrap in d > 2, including rigorous bounds on operator dimensions and operator product expansion (OPE) coefficients [3–32], analytical constraints [33–45], and methods for approximate direct solutions to the bootstrap [46–49], includin”