The (2, 0) superconformal bootstrap

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 operator product expansion (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 light cone expansion of the crossing equation. Our principal result is strong evidence that the A 1 theory realizes the minimal allowed central charge (c ¼ 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 ¼ 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.

Long multiplet bootstrap

“…results in known theories ranging from two-dimensional N = (2, 2) [29], to six-dimensional N = (2, 0) [27] SCFTs. By virtue of exploring the space of SCFTs relying only on symmetries, and with minimum assumptions about the operator content of the theories, the bootstrap program also provides a way to discover new SCFTs.…”

W $$ \mathcal{W} $$ symmetry in six dimensions

“…This is essential information in setting up the conformal bootstrap program [15] for p2, 0q theories, along the lines taken in [16] for N " 4 SCFTs in four dimensions. The application of bootstrap methods to p2, 0q SCFTs will be the subject of a forthcoming publication [17].…”

Towards a tensionless string field theory for the $$ \mathcal{N}=\left(2,0\right) $$ CFT in d = 6

“…When expanded, this implies 18) since the kinematical generators Q K and P have no non-linear parts.…”

“…The bootstrap program [18] is a way of systematically implement these constraints to obtain, in particular, bounds on the spec-…”

“…For other proposals, see [12][13][14][15][16][17] and references therein. Another interesting approach is based on the idea of the conformal bootstrap [18], which does not rely on the existence of a Lagrangian.…”