Carving Out the End of the World or (Superconformal Bootstrap in Six Dimensions)

Abstract

We bootstrap $\mathcal{N}=(1,0)$ superconformal field theories in six dimensions, by analyzing the four-point function of flavor current multiplets. Assuming $E_8$ flavor group, we present universal bounds on the central charge $C_T$ and the flavor central charge $C_J$. Based on the numerical data, we conjecture that the rank-one E-string theory saturates the universal lower bound on $C_J$, and numerically determine the spectrum of long multiplets in the rank-one E-string theory. We comment on the possibility of solving the higher-rank E-string theories by bootstrap and thereby probing M-theory on AdS${}_7\times {\mathrm{S}}^4$/${\mathbb{Z}}_2$.

59 pages, 10 figures, 4 tables; v2-v5: typos corrected, references added