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.
Highlights
AND SUMMARYIn this work we introduce and develop the modern conformal bootstrap program for (2, 0) superconformal theories in six dimensions
We focus on the crossing symmetry constraints that arise from the four-point function of stress tensor multiplets
Expansion (1.3): (i) An infinite set fOχ g of BPS multiplets, whose quantum numbers are known from shortening conditions and whose operator product expansion (OPE) coefficients f ΦΦOχ can be determined in closed form using crossing symmetry, as functions of the central charge c
Summary
In this work we introduce and develop the modern conformal bootstrap program for (2, 0) superconformal theories in six dimensions These theories provide a powerful organizing principle for lower-dimensional supersymmetric dynamics. The six-dimensional (2, 0) theories are singled out as the maximally supersymmetric local conformal field theories (CFTs) in the maximum number of dimensions. The (2, 0) theories are isolated, intrinsically quantum mechanical conformal field theories, which cannot be reached as infrared fixed points of local renormalization group flows starting from a Gaussian fixed point. This is in sharp contrast to more familiar examples of isolated CFTs in lower dimensions, such as the critical. It would be of great interest to develop them further, ideally to the point where quantitative information for the nonprotected operator spectrum could be derived and compared to the bootstrap results obtained here
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