On 5d conformal matter

SCFTs with 8 supercharges lie at the sweet spot of the classification program of susy scale-invariant theories: with this amount of susy, the classification is in principle achievable, despite being non-trivial. In this talk, I will present the geometric approach to the classification of 5d SCFTs, based on geometric engineering on non-compact Calabi-Yau manifolds. The strategy is to imagine a 5d SCFT as a non-Lagrangian generalization of a quiver, and to build this generalised quiver by gauging together indecomposable blocks, called “5d conformal matter theories”. In this talk, I will start with a recap of the geometric construction of [2311.04984]. I will then present some forthcoming results, concerning the (p,q) web realization of 5d conformal matter theories, their reduction to 4d, their magnetic quiver, and the discovery of exotic “trifundamental” and “quadrifundamental” 5d indecomposable blocks (with flavor group at least SO(4k+2)^3 or SO(4k)^4).

In collaboration with M. Del Zotto, M. Graffeo, J. Grimminger, and A. Sangiovanni.