We bootstrap 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×S^4/Z_2.

We construct an index for BPS operators supported on a ray in five dimensional superconformal field theories with exceptional global symmetries. We compute the E_n representations (for n = 2, . . . , 7) of operators of low spin, thus verifying that while the expression for the index is only SO(2n − 2) × U(1) invariant, the index itself exhibits the full E_n symmetry (at least up to the order we expanded). The ray operators we studied in 5d can be viewed as generalizations of operators constructed in a Yang-Mills theory with fundamental matter by attaching an open Wilson line to a quark. For n ≤ 7, in contrast to local operators, they carry nontrivial charge under the ℤ_{9 − n}  ⊂ E_n center of the global symmetry. The representations that appear in the ray operator index are therefore different, for n ≤ 7, from those appearing in the previously computed superconformal index. For 3 ≤ n ≤ 7, we find that the leading term in the index is a character of a minuscule representation of E_n . We also discuss the case n = 8, which presents a unique technical challenge, and remains an open problem.

We present a closed form expression for the semiclassical OPE coefficients that are universal for all 2D CFTs with a “weak” light spectrum, by taking the semiclassical limit of the fusion kernel. We match this with a properly regularized and normalized bulk action evaluated on a geometry with three conical defects, analytically continued in the deficit angles beyond the range for which a metric with positive signature exists. The analytically continued geometry has a codimension-one coordinate singularity surrounding the heaviest conical defect. This singularity becomes a horizon after Wick rotating to Lorentzian signature, suggesting a connection between universality and the existence of a horizon.

We study two-dimensional conformal field theories in the semiclassical limit. In this limit, the four-point function is dominated by intermediate primaries of particular weights along with their descendants, and the crossing equations simplify drastically. For a four-point function receiving sufficiently small contributions from the light primaries, the structure constants involving heavy primaries follow a universal formula. Applying our results to the four-point function of the Z_2 twist field in the symmetric product orbifold, we produce the Hellerman bound and the logarithmically corrected Cardy formula that is valid for h ≥ c/12.

We study tree level scattering amplitudes of four massless states in the double scaled little string theory, and compare them to perturbative loop amplitudes in six-dimensional super-Yang-Mills theory. The little string amplitudes are computed from correlators in the cigar coset CFT and in N = 2 minimal models. The results are expressed in terms of integrals of conformal blocks and evaluated numerically in the α ′ expansion. We find striking agreements with up to 2-loop scattering amplitudes of massless gluons in 6D SU(k) SYM at a ℤ_k invariant point on the Coulomb branch. We comment on the issue of UV divergence at higher loop orders in the gauge theory and discuss the implication of our results.