Carving out the swampland of 6D SCFTs

A tentative classification of 6D Superconformal Field Theories (SCFTs) has recently been obtained via string theory. This geometric engineering of SCFTs offers a complementary way of tackling these mysterious theories to the purely field theoretic methods of the conformal bootstrap. After reviewing the specificities of 6D, we will discuss how to obtain the conformal blocks of four-point functions involving any half-BPS scalar operators, and their symmetries. Finally, we will see how to relate the associated bootstrap bounds to quantities predicted by string theory.