Córdova, Lucía | Search NASA

DOE OSTI2021

The Pollica perspective on the (super)-conformal world

This manuscript samples a series of recent results in the quest for a systematic understanding of the space of conformal field theories, with a particular focus on theories with extended supersymmetry. The large majority of results reported here were presented during the second Pollica summer workshop which took place from June 3–21 2019 and focused on mathematical and geometric tools for superconformal field theories. Furthermore, this manuscript represents in many ways a partial summary of the workshop.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

The O(N) S-matrix monolith

We consider the scattering matrices of massive quantum field theories with no bound states and a global O(N) symmetry in two spacetime dimensions. In particular we explore the space of two-to-two S-matrices of particles of mass m transforming in the vector representation as restricted by the general conditions of unitarity, crossing, analyticity and O(N) symmetry. We found a rich structure in that space by using convex maximization and in particular its convex dual minimization problem. At the boundary of the allowed space special geometric points such as vertices were found to correspond to integrable models. The dual convex minimization problem provides a novel and useful approach to the problem allowing, for example, to prove that generically the S-matrices so obtained saturate unitarity and, insome cases, that they are at vertices of the allowed space.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗